id sid tid token lemma pos ijassa-713 1 1 adv adv PROPN ijassa-713 1 2 syst syst PROPN ijassa-713 1 3 sci sci PROPN ijassa-713 1 4 appl appl PROPN ijassa-713 1 5 2019 2019 NUM ijassa-713 1 6 ; ; PUNCT ijassa-713 1 7 03 03 NUM ijassa-713 1 8 ; ; PUNCT ijassa-713 1 9 52 52 NUM ijassa-713 1 10 - - SYM ijassa-713 1 11 64 64 NUM ijassa-713 1 12 published publish VERB ijassa-713 1 13 online online ADV ijassa-713 1 14 at at ADP ijassa-713 1 15 http://ijassa.ipu.ru/index.php/ijassa/article/view/713 http://ijassa.ipu.ru/index.php/ijassa/article/view/713 NOUN ijassa-713 1 16 optimal optimal ADJ ijassa-713 1 17 values value NOUN ijassa-713 1 18 in in ADP ijassa-713 1 19 an an DET ijassa-713 1 20 uncertain uncertain ADJ ijassa-713 1 21 optimal optimal ADJ ijassa-713 1 22 control control NOUN ijassa-713 1 23 model model NOUN ijassa-713 1 24 with with ADP ijassa-713 1 25 application application NOUN ijassa-713 1 26 to to ADP ijassa-713 1 27 capital capital NOUN ijassa-713 1 28 asset asset NOUN ijassa-713 1 29 management management NOUN ijassa-713 1 30 tolulope tolulope NOUN ijassa-713 1 31 latunde1 latunde1 PROPN ijassa-713 1 32 * * ADJ ijassa-713 1 33 1 1 X ijassa-713 1 34 ) ) PUNCT ijassa-713 1 35 department department NOUN ijassa-713 1 36 of of ADP ijassa-713 1 37 mathematics mathematics PROPN ijassa-713 1 38 , , PUNCT ijassa-713 1 39 federal federal ADJ ijassa-713 1 40 university university NOUN ijassa-713 1 41 , , PUNCT ijassa-713 1 42 oye oye NOUN ijassa-713 1 43 - - PUNCT ijassa-713 1 44 ekiti ekiti PROPN ijassa-713 1 45 , , PUNCT ijassa-713 1 46 nigeria nigeria PROPN ijassa-713 1 47 e e NOUN ijassa-713 1 48 - - NOUN ijassa-713 1 49 mail mail NOUN ijassa-713 1 50 : : PUNCT ijassa-713 1 51 tolulope.latunde@fuoye.edu.ng tolulope.latunde@fuoye.edu.ng NOUN ijassa-713 1 52 received receive VERB ijassa-713 1 53 march march PROPN ijassa-713 1 54 21 21 NUM ijassa-713 1 55 , , PUNCT ijassa-713 1 56 2019 2019 NUM ijassa-713 1 57 ; ; PUNCT ijassa-713 1 58 revised revise VERB ijassa-713 1 59 september september PROPN ijassa-713 1 60 6 6 NUM ijassa-713 1 61 , , PUNCT ijassa-713 1 62 2019 2019 NUM ijassa-713 1 63 ; ; PUNCT ijassa-713 1 64 published publish VERB ijassa-713 1 65 october october PROPN ijassa-713 1 66 1 1 NUM ijassa-713 1 67 , , PUNCT ijassa-713 1 68 2019 2019 NUM ijassa-713 1 69 abstract abstract NOUN ijassa-713 1 70 : : PUNCT ijassa-713 1 71 a a DET ijassa-713 1 72 new new ADJ ijassa-713 1 73 model model NOUN ijassa-713 1 74 of of ADP ijassa-713 1 75 capital capital NOUN ijassa-713 1 76 asset asset NOUN ijassa-713 1 77 management management NOUN ijassa-713 1 78 was be AUX ijassa-713 1 79 developed develop VERB ijassa-713 1 80 under under ADP ijassa-713 1 81 the the DET ijassa-713 1 82 assumptions assumption NOUN ijassa-713 1 83 of of ADP ijassa-713 1 84 hyperbolic hyperbolic ADJ ijassa-713 1 85 absolute absolute ADJ ijassa-713 1 86 risk risk NOUN ijassa-713 1 87 aversion aversion NOUN ijassa-713 1 88 , , PUNCT ijassa-713 1 89 and and CCONJ ijassa-713 1 90 employing employ VERB ijassa-713 1 91 the the DET ijassa-713 1 92 basic basic ADJ ijassa-713 1 93 skills skill NOUN ijassa-713 1 94 of of ADP ijassa-713 1 95 mathematical mathematical ADJ ijassa-713 1 96 modelling modelling NOUN ijassa-713 1 97 . . PUNCT ijassa-713 2 1 the the DET ijassa-713 2 2 solution solution NOUN ijassa-713 2 3 to to ADP ijassa-713 2 4 the the DET ijassa-713 2 5 model model NOUN ijassa-713 2 6 was be AUX ijassa-713 2 7 sought seek VERB ijassa-713 2 8 by by ADP ijassa-713 2 9 formulating formulate VERB ijassa-713 2 10 a a DET ijassa-713 2 11 continuous continuous ADJ ijassa-713 2 12 - - PUNCT ijassa-713 2 13 time time NOUN ijassa-713 2 14 utility utility NOUN ijassa-713 2 15 portfolio portfolio NOUN ijassa-713 2 16 model model NOUN ijassa-713 2 17 satisfying satisfy VERB ijassa-713 2 18 some some DET ijassa-713 2 19 uncertainty uncertainty NOUN ijassa-713 2 20 criteria criterion NOUN ijassa-713 2 21 where where SCONJ ijassa-713 2 22 the the DET ijassa-713 2 23 investment investment NOUN ijassa-713 2 24 is be AUX ijassa-713 2 25 continuous continuous ADJ ijassa-713 2 26 , , PUNCT ijassa-713 2 27 the the DET ijassa-713 2 28 investor investor NOUN ijassa-713 2 29 does do AUX ijassa-713 2 30 not not PART ijassa-713 2 31 possess possess VERB ijassa-713 2 32 enough enough ADJ ijassa-713 2 33 power power NOUN ijassa-713 2 34 to to PART ijassa-713 2 35 determine determine VERB ijassa-713 2 36 price price NOUN ijassa-713 2 37 and and CCONJ ijassa-713 2 38 the the DET ijassa-713 2 39 investor investor NOUN ijassa-713 2 40 can can AUX ijassa-713 2 41 borrow borrow VERB ijassa-713 2 42 money money NOUN ijassa-713 2 43 for for ADP ijassa-713 2 44 a a DET ijassa-713 2 45 given give VERB ijassa-713 2 46 period period NOUN ijassa-713 2 47 at at ADP ijassa-713 2 48 a a DET ijassa-713 2 49 particular particular ADJ ijassa-713 2 50 interest interest NOUN ijassa-713 2 51 rate rate NOUN ijassa-713 2 52 . . PUNCT ijassa-713 3 1 the the DET ijassa-713 3 2 model model NOUN ijassa-713 3 3 was be AUX ijassa-713 3 4 solved solve VERB ijassa-713 3 5 using use VERB ijassa-713 3 6 analytical analytical ADJ ijassa-713 3 7 method method NOUN ijassa-713 3 8 and and CCONJ ijassa-713 3 9 numerical numerical ADJ ijassa-713 3 10 method method NOUN ijassa-713 3 11 and and CCONJ ijassa-713 3 12 optimal optimal ADJ ijassa-713 3 13 values value NOUN ijassa-713 3 14 of of ADP ijassa-713 3 15 some some DET ijassa-713 3 16 input input NOUN ijassa-713 3 17 factors factor NOUN ijassa-713 3 18 are be AUX ijassa-713 3 19 derived derive VERB ijassa-713 3 20 . . PUNCT ijassa-713 4 1 keywords keyword NOUN ijassa-713 4 2 : : PUNCT ijassa-713 4 3 capital capital NOUN ijassa-713 4 4 asset asset NOUN ijassa-713 4 5 management management NOUN ijassa-713 4 6 , , PUNCT ijassa-713 4 7 optimal optimal ADJ ijassa-713 4 8 control control NOUN ijassa-713 4 9 , , PUNCT ijassa-713 4 10 uncertainty uncertainty NOUN ijassa-713 4 11 theory theory NOUN ijassa-713 4 12 , , PUNCT ijassa-713 4 13 optimal optimal ADJ ijassa-713 4 14 values value NOUN ijassa-713 4 15 . . PUNCT ijassa-713 5 1 1 1 X ijassa-713 5 2 . . X ijassa-713 5 3 introduction introduction NOUN ijassa-713 5 4 capital capital NOUN ijassa-713 5 5 asset asset NOUN ijassa-713 5 6 models model NOUN ijassa-713 5 7 have have AUX ijassa-713 5 8 been be AUX ijassa-713 5 9 subject subject ADJ ijassa-713 5 10 to to ADP ijassa-713 5 11 an an DET ijassa-713 5 12 enormous enormous ADJ ijassa-713 5 13 number number NOUN ijassa-713 5 14 of of ADP ijassa-713 5 15 empirical empirical ADJ ijassa-713 5 16 studies study NOUN ijassa-713 5 17 since since SCONJ ijassa-713 5 18 lintner lintner NOUN ijassa-713 5 19 and and CCONJ ijassa-713 5 20 sharpe sharpe NOUN ijassa-713 5 21 in in ADP ijassa-713 5 22 the the DET ijassa-713 5 23 mid-1960 mid-1960 NOUN ijassa-713 5 24 . . PUNCT ijassa-713 6 1 among among ADP ijassa-713 6 2 the the DET ijassa-713 6 3 most most ADV ijassa-713 6 4 notable notable ADJ ijassa-713 6 5 early early ADJ ijassa-713 6 6 tests test NOUN ijassa-713 6 7 of of ADP ijassa-713 6 8 the the DET ijassa-713 6 9 models model NOUN ijassa-713 6 10 are be AUX ijassa-713 6 11 those those PRON ijassa-713 6 12 in in ADP ijassa-713 6 13 [ [ X ijassa-713 6 14 1 1 NUM ijassa-713 6 15 , , PUNCT ijassa-713 6 16 4 4 NUM ijassa-713 6 17 ] ] PUNCT ijassa-713 6 18 . . PUNCT ijassa-713 7 1 other other ADJ ijassa-713 7 2 contributors contributor NOUN ijassa-713 7 3 are be AUX ijassa-713 7 4 included include VERB ijassa-713 7 5 in in ADP ijassa-713 7 6 [ [ X ijassa-713 7 7 3 3 NUM ijassa-713 7 8 , , PUNCT ijassa-713 7 9 5 5 NUM ijassa-713 7 10 , , PUNCT ijassa-713 7 11 13 13 NUM ijassa-713 7 12 , , PUNCT ijassa-713 7 13 14 14 NUM ijassa-713 7 14 ] ] PUNCT ijassa-713 7 15 . . PUNCT ijassa-713 8 1 the the DET ijassa-713 8 2 earliest early ADJ ijassa-713 8 3 researchers researcher NOUN ijassa-713 8 4 found find VERB ijassa-713 8 5 the the DET ijassa-713 8 6 relationships relationship NOUN ijassa-713 8 7 between between ADP ijassa-713 8 8 the the DET ijassa-713 8 9 risk risk NOUN ijassa-713 8 10 - - PUNCT ijassa-713 8 11 free free ADJ ijassa-713 8 12 rate rate NOUN ijassa-713 8 13 and and CCONJ ijassa-713 8 14 market market NOUN ijassa-713 8 15 risk risk NOUN ijassa-713 8 16 premium premium NOUN ijassa-713 8 17 . . PUNCT ijassa-713 9 1 since since SCONJ ijassa-713 9 2 merton merton NOUN ijassa-713 9 3 developed develop VERB ijassa-713 9 4 and and CCONJ ijassa-713 9 5 solve solve VERB ijassa-713 9 6 a a DET ijassa-713 9 7 portfolio portfolio NOUN ijassa-713 9 8 selection selection NOUN ijassa-713 9 9 model model NOUN ijassa-713 9 10 under under ADP ijassa-713 9 11 uncertainty uncertainty NOUN ijassa-713 9 12 for for ADP ijassa-713 9 13 the the DET ijassa-713 9 14 case case NOUN ijassa-713 9 15 of of ADP ijassa-713 9 16 infinite infinite ADJ ijassa-713 9 17 lifetimes lifetime NOUN ijassa-713 9 18 and and CCONJ ijassa-713 9 19 finite finite PROPN ijassa-713 9 20 lifetimes lifetime NOUN ijassa-713 9 21 : : PUNCT ijassa-713 9 22 the the DET ijassa-713 9 23 continuous continuous ADJ ijassa-713 9 24 - - PUNCT ijassa-713 9 25 time time NOUN ijassa-713 9 26 case case NOUN ijassa-713 9 27 for for ADP ijassa-713 9 28 risk risk NOUN ijassa-713 9 29 and and CCONJ ijassa-713 9 30 risk risk NOUN ijassa-713 9 31 - - PUNCT ijassa-713 9 32 free free ADJ ijassa-713 9 33 assets asset NOUN ijassa-713 9 34 , , PUNCT ijassa-713 9 35 capital capital NOUN ijassa-713 9 36 asset asset NOUN ijassa-713 9 37 management management NOUN ijassa-713 9 38 has have AUX ijassa-713 9 39 adapted adapt VERB ijassa-713 9 40 the the DET ijassa-713 9 41 portfolio portfolio NOUN ijassa-713 9 42 theories theory NOUN ijassa-713 9 43 , , PUNCT ijassa-713 9 44 see see VERB ijassa-713 9 45 [ [ X ijassa-713 9 46 12 12 NUM ijassa-713 9 47 ] ] PUNCT ijassa-713 9 48 . . PUNCT ijassa-713 10 1 this this PRON ijassa-713 10 2 results result VERB ijassa-713 10 3 to to ADP ijassa-713 10 4 some some DET ijassa-713 10 5 researchers researcher NOUN ijassa-713 10 6 formulating formulate VERB ijassa-713 10 7 asset asset NOUN ijassa-713 10 8 management management NOUN ijassa-713 10 9 models model NOUN ijassa-713 10 10 using use VERB ijassa-713 10 11 different different ADJ ijassa-713 10 12 mathematical mathematical ADJ ijassa-713 10 13 approaches approach NOUN ijassa-713 10 14 such such ADJ ijassa-713 10 15 that that SCONJ ijassa-713 10 16 optimal optimal ADJ ijassa-713 10 17 values value NOUN ijassa-713 10 18 of of ADP ijassa-713 10 19 controls control NOUN ijassa-713 10 20 and and CCONJ ijassa-713 10 21 input input NOUN ijassa-713 10 22 factors factor NOUN ijassa-713 10 23 are be AUX ijassa-713 10 24 obtained obtain VERB ijassa-713 10 25 . . PUNCT ijassa-713 11 1 a a DET ijassa-713 11 2 stochastic stochastic ADJ ijassa-713 11 3 optimal optimal ADJ ijassa-713 11 4 control control NOUN ijassa-713 11 5 approach approach NOUN ijassa-713 11 6 was be AUX ijassa-713 11 7 utilised utilise VERB ijassa-713 11 8 to to PART ijassa-713 11 9 model model VERB ijassa-713 11 10 debt debt NOUN ijassa-713 11 11 crisis crisis NOUN ijassa-713 11 12 so so SCONJ ijassa-713 11 13 as as SCONJ ijassa-713 11 14 to to PART ijassa-713 11 15 evaluate evaluate VERB ijassa-713 11 16 debt debt NOUN ijassa-713 11 17 crisis crisis NOUN ijassa-713 11 18 in in ADP ijassa-713 11 19 international international ADJ ijassa-713 11 20 finance finance NOUN ijassa-713 11 21 , , PUNCT ijassa-713 11 22 thus thus ADV ijassa-713 11 23 , , PUNCT ijassa-713 11 24 the the DET ijassa-713 11 25 optimal optimal ADJ ijassa-713 11 26 debt debt NOUN ijassa-713 11 27 to to PART ijassa-713 11 28 preclude preclude VERB ijassa-713 11 29 crisis crisis NOUN ijassa-713 11 30 was be AUX ijassa-713 11 31 obtained obtain VERB ijassa-713 11 32 [ [ X ijassa-713 11 33 15 15 NUM ijassa-713 11 34 ] ] PUNCT ijassa-713 11 35 . . PUNCT ijassa-713 12 1 the the DET ijassa-713 12 2 work work NOUN ijassa-713 12 3 [ [ X ijassa-713 12 4 19 19 NUM ijassa-713 12 5 ] ] PUNCT ijassa-713 12 6 was be AUX ijassa-713 12 7 based base VERB ijassa-713 12 8 on on ADP ijassa-713 12 9 the the DET ijassa-713 12 10 concepts concept NOUN ijassa-713 12 11 of of ADP ijassa-713 12 12 uncertainty uncertainty NOUN ijassa-713 12 13 theory theory NOUN ijassa-713 12 14 where where SCONJ ijassa-713 12 15 uncertain uncertain ADJ ijassa-713 12 16 optimal optimal ADJ ijassa-713 12 17 control control NOUN ijassa-713 12 18 was be AUX ijassa-713 12 19 applied apply VERB ijassa-713 12 20 to to PART ijassa-713 12 21 solve solve VERB ijassa-713 12 22 a a DET ijassa-713 12 23 portfolio portfolio NOUN ijassa-713 12 24 selection selection NOUN ijassa-713 12 25 model model NOUN ijassa-713 12 26 and and CCONJ ijassa-713 12 27 obtained obtain VERB ijassa-713 12 28 a a DET ijassa-713 12 29 fundamental fundamental ADJ ijassa-713 12 30 result result NOUN ijassa-713 12 31 called call VERB ijassa-713 12 32 equation equation NOUN ijassa-713 12 33 of of ADP ijassa-713 12 34 optimality optimality NOUN ijassa-713 12 35 for for ADP ijassa-713 12 36 uncertain uncertain ADJ ijassa-713 12 37 optimal optimal ADJ ijassa-713 12 38 control control NOUN ijassa-713 12 39 , , PUNCT ijassa-713 12 40 thus thus ADV ijassa-713 12 41 obtain obtain VERB ijassa-713 12 42 the the DET ijassa-713 12 43 optimal optimal ADJ ijassa-713 12 44 value value NOUN ijassa-713 12 45 of of ADP ijassa-713 12 46 the the DET ijassa-713 12 47 control control NOUN ijassa-713 12 48 . . PUNCT ijassa-713 13 1 formulation formulation NOUN ijassa-713 13 2 of of ADP ijassa-713 13 3 two two NUM ijassa-713 13 4 instances instance NOUN ijassa-713 13 5 of of ADP ijassa-713 13 6 uncertain uncertain ADJ ijassa-713 13 7 multidimensional multidimensional ADJ ijassa-713 13 8 optimal optimal ADJ ijassa-713 13 9 control control NOUN ijassa-713 13 10 models model NOUN ijassa-713 13 11 with with ADP ijassa-713 13 12 𝑛 𝑛 DET ijassa-713 13 13 jumps jump NOUN ijassa-713 13 14 based base VERB ijassa-713 13 15 on on ADP ijassa-713 13 16 uncertainty uncertainty NOUN ijassa-713 13 17 theory theory NOUN ijassa-713 13 18 from from ADP ijassa-713 13 19 the the DET ijassa-713 13 20 perspectives perspective NOUN ijassa-713 13 21 of of ADP ijassa-713 13 22 agents agent NOUN ijassa-713 13 23 ( ( PUNCT ijassa-713 13 24 consumers consumer NOUN ijassa-713 13 25 ) ) PUNCT ijassa-713 13 26 and and CCONJ ijassa-713 13 27 principal principal NOUN ijassa-713 13 28 ( ( PUNCT ijassa-713 13 29 government government NOUN ijassa-713 13 30 ) ) PUNCT ijassa-713 13 31 was be AUX ijassa-713 13 32 carried carry VERB ijassa-713 13 33 out out ADP ijassa-713 13 34 in in ADP ijassa-713 13 35 the the DET ijassa-713 13 36 work work NOUN ijassa-713 13 37 [ [ X ijassa-713 13 38 2 2 X ijassa-713 13 39 ] ] PUNCT ijassa-713 13 40 the the DET ijassa-713 13 41 optimal optimal ADJ ijassa-713 13 42 control control NOUN ijassa-713 13 43 problems problem NOUN ijassa-713 13 44 were be AUX ijassa-713 13 45 applied apply VERB ijassa-713 13 46 to to ADP ijassa-713 13 47 research research NOUN ijassa-713 13 48 and and CCONJ ijassa-713 13 49 development development NOUN ijassa-713 13 50 fiscal fiscal ADJ ijassa-713 13 51 policy policy NOUN ijassa-713 13 52 and and CCONJ ijassa-713 13 53 optimal optimal ADJ ijassa-713 13 54 control control NOUN ijassa-713 13 55 decisions decision NOUN ijassa-713 13 56 were be AUX ijassa-713 13 57 obtained obtain VERB ijassa-713 13 58 . . PUNCT ijassa-713 14 1 it it PRON ijassa-713 14 2 is be AUX ijassa-713 14 3 understood understand VERB ijassa-713 14 4 from from ADP ijassa-713 14 5 existing exist VERB ijassa-713 14 6 works work NOUN ijassa-713 14 7 that that PRON ijassa-713 14 8 the the DET ijassa-713 14 9 research research NOUN ijassa-713 14 10 carried carry VERB ijassa-713 14 11 out out ADP ijassa-713 14 12 in in ADP ijassa-713 14 13 [ [ X ijassa-713 14 14 12,19 12,19 NUM ijassa-713 14 15 , , PUNCT ijassa-713 14 16 2 2 NUM ijassa-713 14 17 ] ] PUNCT ijassa-713 14 18 examined examine VERB ijassa-713 14 19 the the DET ijassa-713 14 20 selection selection NOUN ijassa-713 14 21 of of ADP ijassa-713 14 22 risk risk NOUN ijassa-713 14 23 - - PUNCT ijassa-713 14 24 free free ADJ ijassa-713 14 25 asset asset NOUN ijassa-713 14 26 and and CCONJ ijassa-713 14 27 risk risk NOUN ijassa-713 14 28 asset asset NOUN ijassa-713 14 29 together together ADV ijassa-713 14 30 in in ADP ijassa-713 14 31 the the DET ijassa-713 14 32 formulation formulation NOUN ijassa-713 14 33 of of ADP ijassa-713 14 34 the the DET ijassa-713 14 35 models model NOUN ijassa-713 14 36 . . PUNCT ijassa-713 15 1 meanwhile meanwhile ADV ijassa-713 15 2 , , PUNCT ijassa-713 15 3 it it PRON ijassa-713 15 4 was be AUX ijassa-713 15 5 examined examine VERB ijassa-713 15 6 in in ADP ijassa-713 15 7 [ [ X ijassa-713 15 8 15 15 NUM ijassa-713 15 9 ] ] PUNCT ijassa-713 15 10 , , PUNCT ijassa-713 15 11 the the DET ijassa-713 15 12 selection selection NOUN ijassa-713 15 13 of of ADP ijassa-713 15 14 risky risky ADJ ijassa-713 15 15 assets asset NOUN ijassa-713 15 16 only only ADV ijassa-713 15 17 with with ADP ijassa-713 15 18 stochastic stochastic ADJ ijassa-713 15 19 optimal optimal ADJ ijassa-713 15 20 control control NOUN ijassa-713 15 21 approach approach NOUN ijassa-713 15 22 without without ADP ijassa-713 15 23 considering consider VERB ijassa-713 15 24 depreciation depreciation NOUN ijassa-713 15 25 and and CCONJ ijassa-713 15 26 taxation taxation NOUN ijassa-713 15 27 as as ADP ijassa-713 15 28 input input NOUN ijassa-713 15 29 factors factor NOUN ijassa-713 15 30 . . PUNCT ijassa-713 16 1 the the DET ijassa-713 16 2 choice choice NOUN ijassa-713 16 3 of of ADP ijassa-713 16 4 uncertainty uncertainty NOUN ijassa-713 16 5 theory theory NOUN ijassa-713 16 6 over over ADP ijassa-713 16 7 the the DET ijassa-713 16 8 conventional conventional ADJ ijassa-713 16 9 probability probability NOUN ijassa-713 16 10 theory theory NOUN ijassa-713 16 11 exists exist VERB ijassa-713 16 12 when when SCONJ ijassa-713 16 13 the the DET ijassa-713 16 14 sample sample NOUN ijassa-713 16 15 size size NOUN ijassa-713 16 16 is be AUX ijassa-713 16 17 * * PUNCT ijassa-713 16 18 corresponding correspond VERB ijassa-713 16 19 author author NOUN ijassa-713 16 20 : : PUNCT ijassa-713 16 21 tolulope.latunde@fuoye.edu.ng tolulope.latunde@fuoye.edu.ng NOUN ijassa-713 16 22 mailto:tolulope.latunde@fuoye.edu.ng mailto:tolulope.latunde@fuoye.edu.ng NOUN ijassa-713 16 23 t. t. NOUN ijassa-713 16 24 latunde latunde VERB ijassa-713 16 25 53 53 NUM ijassa-713 16 26 copyright copyright NOUN ijassa-713 16 27 Β© Β© PROPN ijassa-713 16 28 2019 2019 NUM ijassa-713 16 29 assa assa NOUN ijassa-713 16 30 . . PUNCT ijassa-713 17 1 adv adv PROPN ijassa-713 17 2 . . PUNCT ijassa-713 18 1 in in ADP ijassa-713 18 2 systems system NOUN ijassa-713 18 3 science science NOUN ijassa-713 18 4 and and CCONJ ijassa-713 18 5 appl appl NOUN ijassa-713 18 6 . . PUNCT ijassa-713 19 1 ( ( PUNCT ijassa-713 19 2 2019 2019 NUM ijassa-713 19 3 ) ) PUNCT ijassa-713 19 4 small small ADJ ijassa-713 19 5 to to PART ijassa-713 19 6 estimate estimate VERB ijassa-713 19 7 a a DET ijassa-713 19 8 probability probability NOUN ijassa-713 19 9 distribution distribution NOUN ijassa-713 19 10 and and CCONJ ijassa-713 19 11 degree degree NOUN ijassa-713 19 12 belief belief NOUN ijassa-713 19 13 are be AUX ijassa-713 19 14 ascertained ascertain VERB ijassa-713 19 15 from from ADP ijassa-713 19 16 experts expert NOUN ijassa-713 19 17 to to PART ijassa-713 19 18 work work VERB ijassa-713 19 19 in in ADP ijassa-713 19 20 place place NOUN ijassa-713 19 21 of of ADP ijassa-713 19 22 frequency frequency NOUN ijassa-713 19 23 since since SCONJ ijassa-713 19 24 human human ADJ ijassa-713 19 25 beings being NOUN ijassa-713 19 26 always always ADV ijassa-713 19 27 overweight overweight VERB ijassa-713 19 28 unlikely unlikely ADJ ijassa-713 19 29 events event NOUN ijassa-713 19 30 consequently consequently ADV ijassa-713 19 31 , , PUNCT ijassa-713 19 32 a a DET ijassa-713 19 33 new new ADJ ijassa-713 19 34 model model NOUN ijassa-713 19 35 of of ADP ijassa-713 19 36 asset asset NOUN ijassa-713 19 37 management management NOUN ijassa-713 19 38 based base VERB ijassa-713 19 39 on on ADP ijassa-713 19 40 uncertainty uncertainty NOUN ijassa-713 19 41 theory theory NOUN ijassa-713 19 42 was be AUX ijassa-713 19 43 formulated formulate VERB ijassa-713 19 44 in in ADP ijassa-713 19 45 [ [ X ijassa-713 19 46 6 6 NUM ijassa-713 19 47 ] ] PUNCT ijassa-713 19 48 where where SCONJ ijassa-713 19 49 the the DET ijassa-713 19 50 selection selection NOUN ijassa-713 19 51 of of ADP ijassa-713 19 52 capital capital NOUN ijassa-713 19 53 assets asset NOUN ijassa-713 19 54 , , PUNCT ijassa-713 19 55 classified classify VERB ijassa-713 19 56 as as SCONJ ijassa-713 19 57 risky risky ADJ ijassa-713 19 58 assets asset NOUN ijassa-713 19 59 is be AUX ijassa-713 19 60 examined examine VERB ijassa-713 19 61 . . PUNCT ijassa-713 20 1 thus thus ADV ijassa-713 20 2 , , PUNCT ijassa-713 20 3 depreciation depreciation NOUN ijassa-713 20 4 and and CCONJ ijassa-713 20 5 taxation taxation NOUN ijassa-713 20 6 are be AUX ijassa-713 20 7 considered consider VERB ijassa-713 20 8 as as ADP ijassa-713 20 9 input input NOUN ijassa-713 20 10 factors factor NOUN ijassa-713 20 11 in in ADP ijassa-713 20 12 the the DET ijassa-713 20 13 formulation formulation NOUN ijassa-713 20 14 of of ADP ijassa-713 20 15 the the DET ijassa-713 20 16 models model NOUN ijassa-713 20 17 . . PUNCT ijassa-713 21 1 however however ADV ijassa-713 21 2 , , PUNCT ijassa-713 21 3 this this DET ijassa-713 21 4 work work NOUN ijassa-713 21 5 is be AUX ijassa-713 21 6 an an DET ijassa-713 21 7 extension extension NOUN ijassa-713 21 8 of of ADP ijassa-713 21 9 the the DET ijassa-713 21 10 work work NOUN ijassa-713 21 11 [ [ X ijassa-713 21 12 6 6 NUM ijassa-713 21 13 , , PUNCT ijassa-713 21 14 7 7 NUM ijassa-713 21 15 ] ] PUNCT ijassa-713 21 16 such such ADJ ijassa-713 21 17 that that SCONJ ijassa-713 21 18 we we PRON ijassa-713 21 19 seek seek VERB ijassa-713 21 20 to to PART ijassa-713 21 21 provide provide VERB ijassa-713 21 22 solutions solution NOUN ijassa-713 21 23 to to ADP ijassa-713 21 24 a a DET ijassa-713 21 25 problem problem NOUN ijassa-713 21 26 of of ADP ijassa-713 21 27 capital capital NOUN ijassa-713 21 28 assets asset NOUN ijassa-713 21 29 using use VERB ijassa-713 21 30 a a DET ijassa-713 21 31 real real ADJ ijassa-713 21 32 life life NOUN ijassa-713 21 33 situation situation NOUN ijassa-713 21 34 . . PUNCT ijassa-713 22 1 the the DET ijassa-713 22 2 proposed propose VERB ijassa-713 22 3 model model NOUN ijassa-713 22 4 deals deal NOUN ijassa-713 22 5 with with ADP ijassa-713 22 6 a a DET ijassa-713 22 7 case case NOUN ijassa-713 22 8 where where SCONJ ijassa-713 22 9 a a DET ijassa-713 22 10 nation nation NOUN ijassa-713 22 11 invests invest VERB ijassa-713 22 12 her her PRON ijassa-713 22 13 wealth wealth NOUN ijassa-713 22 14 in in ADP ijassa-713 22 15 capital capital NOUN ijassa-713 22 16 assets asset NOUN ijassa-713 22 17 , , PUNCT ijassa-713 22 18 for for ADP ijassa-713 22 19 a a DET ijassa-713 22 20 particular particular ADJ ijassa-713 22 21 period period NOUN ijassa-713 22 22 of of ADP ijassa-713 22 23 time time NOUN ijassa-713 22 24 . . PUNCT ijassa-713 23 1 it it PRON ijassa-713 23 2 is be AUX ijassa-713 23 3 assumed assume VERB ijassa-713 23 4 that that SCONJ ijassa-713 23 5 there there PRON ijassa-713 23 6 is be VERB ijassa-713 23 7 difficulty difficulty NOUN ijassa-713 23 8 in in ADP ijassa-713 23 9 deciding decide VERB ijassa-713 23 10 the the DET ijassa-713 23 11 fraction fraction NOUN ijassa-713 23 12 of of ADP ijassa-713 23 13 the the DET ijassa-713 23 14 nation nation NOUN ijassa-713 23 15 ’s ’s PART ijassa-713 23 16 net net ADJ ijassa-713 23 17 worth worth NOUN ijassa-713 23 18 to to PART ijassa-713 23 19 be be AUX ijassa-713 23 20 incurred incur VERB ijassa-713 23 21 on on ADP ijassa-713 23 22 the the DET ijassa-713 23 23 investments investment NOUN ijassa-713 23 24 of of ADP ijassa-713 23 25 capital capital NOUN ijassa-713 23 26 assets asset NOUN ijassa-713 23 27 , , PUNCT ijassa-713 23 28 thus thus ADV ijassa-713 23 29 leading lead VERB ijassa-713 23 30 to to ADP ijassa-713 23 31 the the DET ijassa-713 23 32 problem problem NOUN ijassa-713 23 33 of of ADP ijassa-713 23 34 how how SCONJ ijassa-713 23 35 to to PART ijassa-713 23 36 optimize optimize VERB ijassa-713 23 37 the the DET ijassa-713 23 38 expected expect VERB ijassa-713 23 39 present present ADJ ijassa-713 23 40 value value NOUN ijassa-713 23 41 of of ADP ijassa-713 23 42 the the DET ijassa-713 23 43 utility utility NOUN ijassa-713 23 44 of of ADP ijassa-713 23 45 assets asset NOUN ijassa-713 23 46 . . PUNCT ijassa-713 24 1 2 2 X ijassa-713 24 2 . . X ijassa-713 24 3 preliminary preliminary ADJ ijassa-713 24 4 uncertainty uncertainty NOUN ijassa-713 24 5 theory theory NOUN ijassa-713 24 6 is be AUX ijassa-713 24 7 a a DET ijassa-713 24 8 branch branch NOUN ijassa-713 24 9 of of ADP ijassa-713 24 10 mathematics mathematic NOUN ijassa-713 24 11 for for ADP ijassa-713 24 12 modelling model VERB ijassa-713 24 13 belief belief NOUN ijassa-713 24 14 degrees degree NOUN ijassa-713 24 15 established establish VERB ijassa-713 24 16 by by ADP ijassa-713 24 17 liu liu PROPN ijassa-713 24 18 , , PUNCT ijassa-713 24 19 [ [ X ijassa-713 24 20 8 8 NUM ijassa-713 24 21 ] ] PUNCT ijassa-713 24 22 and and CCONJ ijassa-713 24 23 refined refine VERB ijassa-713 24 24 in in ADP ijassa-713 24 25 [ [ X ijassa-713 24 26 11 11 NUM ijassa-713 24 27 ] ] PUNCT ijassa-713 24 28 . . PUNCT ijassa-713 25 1 the the DET ijassa-713 25 2 choice choice NOUN ijassa-713 25 3 of of ADP ijassa-713 25 4 uncertainty uncertainty NOUN ijassa-713 25 5 theory theory NOUN ijassa-713 25 6 over over ADP ijassa-713 25 7 the the DET ijassa-713 25 8 conventional conventional ADJ ijassa-713 25 9 probability probability NOUN ijassa-713 25 10 theory theory NOUN ijassa-713 25 11 exists exist VERB ijassa-713 25 12 when when SCONJ ijassa-713 25 13 the the DET ijassa-713 25 14 sample sample NOUN ijassa-713 25 15 size size NOUN ijassa-713 25 16 is be AUX ijassa-713 25 17 small small ADJ ijassa-713 25 18 to to PART ijassa-713 25 19 estimate estimate VERB ijassa-713 25 20 a a DET ijassa-713 25 21 probability probability NOUN ijassa-713 25 22 distribution distribution NOUN ijassa-713 25 23 and and CCONJ ijassa-713 25 24 degree degree NOUN ijassa-713 25 25 belief belief NOUN ijassa-713 25 26 are be AUX ijassa-713 25 27 ascertained ascertain VERB ijassa-713 25 28 from from ADP ijassa-713 25 29 experts expert NOUN ijassa-713 25 30 to to PART ijassa-713 25 31 work work VERB ijassa-713 25 32 in in ADP ijassa-713 25 33 place place NOUN ijassa-713 25 34 of of ADP ijassa-713 25 35 frequency frequency NOUN ijassa-713 25 36 since since SCONJ ijassa-713 25 37 human human ADJ ijassa-713 25 38 beings being NOUN ijassa-713 25 39 always always ADV ijassa-713 25 40 overweight overweight VERB ijassa-713 25 41 unlikely unlikely ADJ ijassa-713 25 42 events event NOUN ijassa-713 25 43 . . PUNCT ijassa-713 26 1 for for ADP ijassa-713 26 2 the the DET ijassa-713 26 3 sake sake NOUN ijassa-713 26 4 of of ADP ijassa-713 26 5 this this DET ijassa-713 26 6 work work NOUN ijassa-713 26 7 , , PUNCT ijassa-713 26 8 the the DET ijassa-713 26 9 following follow VERB ijassa-713 26 10 concepts concept NOUN ijassa-713 26 11 are be AUX ijassa-713 26 12 utilized utilize VERB ijassa-713 26 13 . . PUNCT ijassa-713 27 1 let let VERB ijassa-713 27 2 Ξ³ Ξ³ NOUN ijassa-713 27 3 be be AUX ijassa-713 27 4 a a DET ijassa-713 27 5 nonempty nonempty ADV ijassa-713 27 6 set set VERB ijassa-713 27 7 and and CCONJ ijassa-713 27 8 𝐿 𝐿 PROPN ijassa-713 27 9 a a DET ijassa-713 27 10 𝜎algebra 𝜎algebra NOUN ijassa-713 27 11 over over ADP ijassa-713 27 12 Ξ³ Ξ³ PROPN ijassa-713 27 13 such such ADJ ijassa-713 27 14 that that SCONJ ijassa-713 27 15 ( ( PUNCT ijassa-713 27 16 Ξ³ Ξ³ X ijassa-713 27 17 , , PUNCT ijassa-713 27 18 𝐿 𝐿 PROPN ijassa-713 27 19 ) ) PUNCT ijassa-713 27 20 be be VERB ijassa-713 27 21 a a DET ijassa-713 27 22 measurable measurable ADJ ijassa-713 27 23 space space NOUN ijassa-713 27 24 . . PUNCT ijassa-713 28 1 each each DET ijassa-713 28 2 element element NOUN ijassa-713 28 3 Ξ» Ξ» PROPN ijassa-713 28 4 ∈ ∈ PROPN ijassa-713 28 5 𝐿 𝐿 PROPN ijassa-713 28 6 is be AUX ijassa-713 28 7 called call VERB ijassa-713 28 8 an an DET ijassa-713 28 9 event event NOUN ijassa-713 28 10 . . PUNCT ijassa-713 29 1 definition definition NOUN ijassa-713 29 2 2.1 2.1 NUM ijassa-713 30 1 [ [ X ijassa-713 30 2 8 8 NUM ijassa-713 30 3 ] ] X ijassa-713 30 4 : : PUNCT ijassa-713 30 5 a a DET ijassa-713 30 6 set set NOUN ijassa-713 30 7 function function NOUN ijassa-713 30 8 𝑀 𝑀 PROPN ijassa-713 30 9 defined define VERB ijassa-713 30 10 on on ADP ijassa-713 30 11 the the DET ijassa-713 30 12 𝜎-algebra 𝜎-algebra PROPN ijassa-713 30 13 over over ADP ijassa-713 30 14 𝐿 𝐿 PROPN ijassa-713 30 15 is be AUX ijassa-713 30 16 called call VERB ijassa-713 30 17 an an DET ijassa-713 30 18 uncertain uncertain ADJ ijassa-713 30 19 measure measure NOUN ijassa-713 30 20 if if SCONJ ijassa-713 30 21 it it PRON ijassa-713 30 22 satisfies satisfy VERB ijassa-713 30 23 the the DET ijassa-713 30 24 following follow VERB ijassa-713 30 25 axioms axiom NOUN ijassa-713 30 26 : : PUNCT ijassa-713 30 27 axiom axiom NOUN ijassa-713 30 28 1 1 NUM ijassa-713 30 29 . . PUNCT ijassa-713 31 1 ( ( PUNCT ijassa-713 31 2 normality normality NOUN ijassa-713 31 3 axiom axiom NOUN ijassa-713 31 4 ): ): PUNCT ijassa-713 31 5 𝑀{Ξ» 𝑀{Ξ» PRON ijassa-713 31 6 } } PUNCT ijassa-713 31 7 = = SYM ijassa-713 31 8 1 1 NUM ijassa-713 31 9 for for ADP ijassa-713 31 10 the the DET ijassa-713 31 11 universal universal ADJ ijassa-713 31 12 set set VERB ijassa-713 31 13 𝛀. 𝛀. PROPN ijassa-713 31 14 axiom axiom NOUN ijassa-713 31 15 2 2 NUM ijassa-713 31 16 . . PUNCT ijassa-713 32 1 ( ( PUNCT ijassa-713 32 2 duality duality NOUN ijassa-713 32 3 axiom axiom NOUN ijassa-713 32 4 ): ): PUNCT ijassa-713 32 5 𝑀{Ξ» 𝑀{Ξ» PRON ijassa-713 32 6 } } PUNCT ijassa-713 32 7 + + CCONJ ijassa-713 32 8 𝑀{λ𝑐 𝑀{λ𝑐 PROPN ijassa-713 32 9 } } PUNCT ijassa-713 32 10 = = SYM ijassa-713 32 11 1 1 NUM ijassa-713 32 12 for for ADP ijassa-713 32 13 any any DET ijassa-713 32 14 event event NOUN ijassa-713 32 15 Ξ» Ξ» PROPN ijassa-713 32 16 . . PROPN ijassa-713 32 17 axiom axiom PROPN ijassa-713 32 18 3 3 NUM ijassa-713 32 19 . . PUNCT ijassa-713 33 1 ( ( PUNCT ijassa-713 33 2 subadditivity subadditivity NOUN ijassa-713 33 3 axiom axiom NOUN ijassa-713 33 4 ): ): PUNCT ijassa-713 33 5 for for ADP ijassa-713 33 6 every every DET ijassa-713 33 7 countable countable ADJ ijassa-713 33 8 sequence sequence NOUN ijassa-713 33 9 of of ADP ijassa-713 33 10 events event NOUN ijassa-713 33 11 , , PUNCT ijassa-713 33 12 Ξ»1 Ξ»1 ADJ ijassa-713 33 13 , , PUNCT ijassa-713 33 14 Ξ»2 Ξ»2 NOUN ijassa-713 33 15 , , PUNCT ijassa-713 33 16 β‹― β‹― PROPN ijassa-713 33 17 , , PUNCT ijassa-713 33 18 we we PRON ijassa-713 33 19 have have AUX ijassa-713 33 20 𝑀{β‹ƒβˆž 𝑀{β‹ƒβˆž ADJ ijassa-713 33 21 𝑖=1 𝑖=1 PUNCT ijassa-713 33 22 λ𝑖 λ𝑖 CCONJ ijassa-713 33 23 } } PUNCT ijassa-713 33 24 ≀ ≀ NUM ijassa-713 33 25 βˆ‘βˆž βˆ‘βˆž NOUN ijassa-713 33 26 𝑖=1 𝑖=1 PUNCT ijassa-713 33 27 𝑀{λ𝑖 𝑀{λ𝑖 NOUN ijassa-713 33 28 } } PUNCT ijassa-713 33 29 ( ( PUNCT ijassa-713 33 30 2.1 2.1 NUM ijassa-713 33 31 ) ) PUNCT ijassa-713 33 32 axiom axiom NOUN ijassa-713 33 33 4 4 NUM ijassa-713 33 34 . . PUNCT ijassa-713 34 1 ( ( PUNCT ijassa-713 34 2 product product NOUN ijassa-713 34 3 axiom axiom NOUN ijassa-713 34 4 ): ): PUNCT ijassa-713 34 5 let let VERB ijassa-713 34 6 ( ( PUNCT ijassa-713 34 7 Ξ³π‘˜ Ξ³π‘˜ INTJ ijassa-713 34 8 , , PUNCT ijassa-713 34 9 πΏπ‘˜ πΏπ‘˜ PROPN ijassa-713 34 10 , , PUNCT ijassa-713 34 11 π‘€π‘˜ π‘€π‘˜ PROPN ijassa-713 34 12 ) ) PUNCT ijassa-713 34 13 be be VERB ijassa-713 34 14 uncertainty uncertainty NOUN ijassa-713 34 15 spaces space NOUN ijassa-713 34 16 for for ADP ijassa-713 34 17 π‘˜ π‘˜ PRON ijassa-713 34 18 = = SYM ijassa-713 34 19 1,2 1,2 NUM ijassa-713 34 20 , , PUNCT ijassa-713 34 21 β‹―the β‹―the DET ijassa-713 34 22 product product NOUN ijassa-713 34 23 uncertain uncertain ADJ ijassa-713 34 24 measure measure NOUN ijassa-713 34 25 𝑀 𝑀 PROPN ijassa-713 34 26 is be AUX ijassa-713 34 27 an an DET ijassa-713 34 28 uncertain uncertain ADJ ijassa-713 34 29 measure measure NOUN ijassa-713 34 30 satisfying satisfy VERB ijassa-713 34 31 𝑀{∏∞ 𝑀{∏∞ PUNCT ijassa-713 35 1 π‘˜=1 π‘˜=1 X ijassa-713 36 1 Ξ»π‘˜ Ξ»π‘˜ AUX ijassa-713 36 2 } } PUNCT ijassa-713 36 3 = = SYM ijassa-713 36 4 min1β‰€π‘˜β‰€βˆžπ‘€π‘˜{Ξ»π‘˜ min1β‰€π‘˜β‰€βˆžπ‘€π‘˜{Ξ»π‘˜ PROPN ijassa-713 36 5 } } PUNCT ijassa-713 36 6 ( ( PUNCT ijassa-713 36 7 2.2 2.2 NUM ijassa-713 36 8 ) ) PUNCT ijassa-713 36 9 where where SCONJ ijassa-713 36 10 Ξ»π‘˜ Ξ»π‘˜ NOUN ijassa-713 36 11 are be AUX ijassa-713 36 12 arbitrarily arbitrarily ADV ijassa-713 36 13 chosen choose VERB ijassa-713 36 14 events event NOUN ijassa-713 36 15 from from ADP ijassa-713 36 16 πΏπ‘˜ πΏπ‘˜ PROPN ijassa-713 36 17 for for ADP ijassa-713 36 18 π‘˜ π‘˜ X ijassa-713 36 19 = = SYM ijassa-713 36 20 1,2 1,2 NUM ijassa-713 36 21 , , PUNCT ijassa-713 36 22 β‹― β‹― NOUN ijassa-713 36 23 , , PUNCT ijassa-713 36 24 respectively respectively ADV ijassa-713 36 25 . . PUNCT ijassa-713 37 1 definition definition NOUN ijassa-713 37 2 2.2 2.2 NUM ijassa-713 38 1 [ [ SYM ijassa-713 38 2 10 10 NUM ijassa-713 38 3 ] ] X ijassa-713 38 4 : : PUNCT ijassa-713 38 5 an an DET ijassa-713 38 6 uncertain uncertain ADJ ijassa-713 38 7 process process NOUN ijassa-713 38 8 𝐢𝜎 𝐢𝜎 NOUN ijassa-713 38 9 is be AUX ijassa-713 38 10 said say VERB ijassa-713 38 11 to to PART ijassa-713 38 12 be be AUX ijassa-713 38 13 a a DET ijassa-713 38 14 canonical canonical ADJ ijassa-713 38 15 liu liu NOUN ijassa-713 38 16 process process NOUN ijassa-713 38 17 if if SCONJ ijassa-713 38 18 ( ( PUNCT ijassa-713 38 19 i i NOUN ijassa-713 38 20 ) ) PUNCT ijassa-713 38 21 𝐢0 𝐢0 PROPN ijassa-713 38 22 = = PUNCT ijassa-713 38 23 0 0 NUM ijassa-713 38 24 and and CCONJ ijassa-713 38 25 almost almost ADV ijassa-713 38 26 all all PRON ijassa-713 38 27 sample sample NOUN ijassa-713 38 28 paths path NOUN ijassa-713 38 29 are be AUX ijassa-713 38 30 lipschitz lipschitz VERB ijassa-713 39 1 continuous continuous ADJ ijassa-713 39 2 , , PUNCT ijassa-713 39 3 ( ( PUNCT ijassa-713 39 4 ii ii NOUN ijassa-713 39 5 ) ) PUNCT ijassa-713 39 6 𝐢𝜎 𝐢𝜎 PROPN ijassa-713 39 7 has have VERB ijassa-713 39 8 stationary stationary ADJ ijassa-713 39 9 and and CCONJ ijassa-713 39 10 independent independent ADJ ijassa-713 39 11 increments increment NOUN ijassa-713 39 12 , , PUNCT ijassa-713 39 13 ( ( PUNCT ijassa-713 39 14 iii iii X ijassa-713 39 15 ) ) PUNCT ijassa-713 39 16 every every DET ijassa-713 39 17 increment increment NOUN ijassa-713 39 18 𝐢𝑠+𝜎 𝐢𝑠+𝜎 NOUN ijassa-713 39 19 βˆ’ βˆ’ PROPN ijassa-713 40 1 𝐢𝑠 𝐢𝑠 PROPN ijassa-713 40 2 is be AUX ijassa-713 40 3 a a DET ijassa-713 40 4 normal normal ADJ ijassa-713 40 5 uncertain uncertain ADJ ijassa-713 40 6 variable variable NOUN ijassa-713 40 7 with with ADP ijassa-713 40 8 expected expect VERB ijassa-713 40 9 value value NOUN ijassa-713 40 10 0 0 NUM ijassa-713 40 11 and and CCONJ ijassa-713 40 12 variance variance NOUN ijassa-713 40 13 𝜎2 𝜎2 NOUN ijassa-713 40 14 . . PUNCT ijassa-713 41 1 the the DET ijassa-713 41 2 uncertainty uncertainty NOUN ijassa-713 41 3 distribution distribution NOUN ijassa-713 41 4 of of ADP ijassa-713 41 5 𝐢𝜎 𝐢𝜎 PROPN ijassa-713 41 6 is be AUX ijassa-713 41 7 Ο†πœŽ(π‘₯ Ο†πœŽ(π‘₯ NUM ijassa-713 41 8 ) ) PUNCT ijassa-713 41 9 = = NOUN ijassa-713 42 1 [ [ X ijassa-713 42 2 1 1 NUM ijassa-713 42 3 + + NUM ijassa-713 42 4 exp exp NOUN ijassa-713 42 5 ( ( PUNCT ijassa-713 42 6 βˆ’πœ‹π‘₯ βˆ’πœ‹π‘₯ NOUN ijassa-713 42 7 √3𝜎 √3𝜎 NUM ijassa-713 42 8 ) ) PUNCT ijassa-713 42 9 ] ] PUNCT ijassa-713 43 1 βˆ’1 βˆ’1 NOUN ijassa-713 43 2 , , PUNCT ijassa-713 43 3 π‘₯ π‘₯ DET ijassa-713 43 4 ∈ ∈ PROPN ijassa-713 43 5 β„œ β„œ PROPN ijassa-713 43 6 ( ( PUNCT ijassa-713 43 7 2.3 2.3 NUM ijassa-713 43 8 ) ) PUNCT ijassa-713 43 9 and and CCONJ ijassa-713 43 10 the the DET ijassa-713 43 11 inverse inverse NOUN ijassa-713 43 12 distribution distribution NOUN ijassa-713 43 13 is be AUX ijassa-713 43 14 Ο†πœŽ Ο†πœŽ ADP ijassa-713 43 15 βˆ’1(𝑦 βˆ’1(𝑦 NOUN ijassa-713 43 16 ) ) PUNCT ijassa-713 43 17 = = SYM ijassa-713 44 1 𝜎√3 𝜎√3 PROPN ijassa-713 44 2 πœ‹ πœ‹ X ijassa-713 44 3 ln ln PROPN ijassa-713 44 4 𝑦 𝑦 NOUN ijassa-713 44 5 1βˆ’π‘¦ 1βˆ’π‘¦ NUM ijassa-713 44 6 , , PUNCT ijassa-713 44 7 𝑦 𝑦 NOUN ijassa-713 44 8 ∈ ∈ PROPN ijassa-713 44 9 β„œ β„œ PROPN ijassa-713 44 10 ( ( PUNCT ijassa-713 44 11 2.4 2.4 NUM ijassa-713 44 12 ) ) PUNCT ijassa-713 44 13 definition definition NOUN ijassa-713 44 14 2.3 2.3 NUM ijassa-713 45 1 [ [ NOUN ijassa-713 45 2 8 8 NUM ijassa-713 45 3 ] ] PUNCT ijassa-713 45 4 : : PUNCT ijassa-713 45 5 let let VERB ijassa-713 45 6 πœ‰ πœ‰ PART ijassa-713 45 7 be be AUX ijassa-713 45 8 an an DET ijassa-713 45 9 uncertain uncertain ADJ ijassa-713 45 10 variable variable NOUN ijassa-713 45 11 . . PUNCT ijassa-713 46 1 then then ADV ijassa-713 46 2 the the DET ijassa-713 46 3 expected expect VERB ijassa-713 46 4 value value NOUN ijassa-713 46 5 of of ADP ijassa-713 46 6 πœ‰ πœ‰ NOUN ijassa-713 46 7 is be AUX ijassa-713 46 8 defined define VERB ijassa-713 46 9 by by ADP ijassa-713 46 10 𝐸[πœ‰ 𝐸[πœ‰ NOUN ijassa-713 46 11 ] ] PUNCT ijassa-713 47 1 = = PUNCT ijassa-713 47 2 ∫ ∫ PROPN ijassa-713 48 1 + + NUM ijassa-713 48 2 ∞ ∞ PROPN ijassa-713 48 3 0 0 NUM ijassa-713 48 4 𝑀{πœ‰ 𝑀{πœ‰ NOUN ijassa-713 48 5 β‰₯ β‰₯ NUM ijassa-713 48 6 π‘₯}𝑑π‘₯ π‘₯}𝑑π‘₯ NUM ijassa-713 48 7 βˆ’ βˆ’ PROPN ijassa-713 48 8 ∫ ∫ PROPN ijassa-713 48 9 0 0 NUM ijassa-713 49 1 βˆ’βˆž βˆ’βˆž ADP ijassa-713 49 2 𝑀{πœ‰ 𝑀{πœ‰ PROPN ijassa-713 49 3 ≀ ≀ NUM ijassa-713 49 4 π‘₯}𝑑π‘₯ π‘₯}𝑑π‘₯ NUM ijassa-713 49 5 ( ( PUNCT ijassa-713 49 6 2.5 2.5 NUM ijassa-713 49 7 ) ) PUNCT ijassa-713 49 8 provided provide VERB ijassa-713 49 9 that that SCONJ ijassa-713 49 10 at at ADV ijassa-713 49 11 least least ADJ ijassa-713 49 12 one one NUM ijassa-713 49 13 of of ADP ijassa-713 49 14 the the DET ijassa-713 49 15 two two NUM ijassa-713 49 16 integrals integral NOUN ijassa-713 49 17 is be AUX ijassa-713 49 18 finite finite ADJ ijassa-713 49 19 definition definition NOUN ijassa-713 49 20 2.4 2.4 NUM ijassa-713 49 21 [ [ SYM ijassa-713 49 22 9 9 NUM ijassa-713 49 23 ] ] SYM ijassa-713 49 24 : : PUNCT ijassa-713 49 25 an an DET ijassa-713 49 26 uncertain uncertain ADJ ijassa-713 49 27 process process NOUN ijassa-713 49 28 𝑋𝑑 𝑋𝑑 PROPN ijassa-713 49 29 is be AUX ijassa-713 49 30 said say VERB ijassa-713 49 31 to to PART ijassa-713 49 32 have have VERB ijassa-713 49 33 independent independent ADJ ijassa-713 49 34 increments increment NOUN ijassa-713 49 35 if if SCONJ ijassa-713 49 36 𝑋𝑑1 𝑋𝑑1 ADJ ijassa-713 49 37 βˆ’ βˆ’ PROPN ijassa-713 49 38 𝑋𝑑0 𝑋𝑑0 NOUN ijassa-713 49 39 , , PUNCT ijassa-713 49 40 𝑋𝑑2 𝑋𝑑2 NOUN ijassa-713 49 41 βˆ’ βˆ’ PROPN ijassa-713 49 42 𝑋𝑑1 𝑋𝑑1 NOUN ijassa-713 49 43 , , PUNCT ijassa-713 49 44 β‹― β‹― PROPN ijassa-713 49 45 , , PUNCT ijassa-713 49 46 π‘‹π‘‘π‘˜ π‘‹π‘‘π‘˜ PROPN ijassa-713 49 47 βˆ’ βˆ’ PROPN ijassa-713 49 48 π‘‹π‘‘π‘˜βˆ’1 π‘‹π‘‘π‘˜βˆ’1 VERB ijassa-713 49 49 54 54 NUM ijassa-713 49 50 optimal optimal ADJ ijassa-713 49 51 values value NOUN ijassa-713 49 52 in in ADP ijassa-713 49 53 uncertin uncertin PROPN ijassa-713 49 54 optimal optimal ADJ ijassa-713 49 55 control control NOUN ijassa-713 49 56 model model NOUN ijassa-713 49 57 copyright copyright NOUN ijassa-713 49 58 Β© Β© PROPN ijassa-713 49 59 2019 2019 NUM ijassa-713 49 60 assa assa PROPN ijassa-713 49 61 adv adv PROPN ijassa-713 49 62 . . PUNCT ijassa-713 50 1 in in ADP ijassa-713 50 2 systems system NOUN ijassa-713 50 3 science science NOUN ijassa-713 50 4 and and CCONJ ijassa-713 50 5 appl appl NOUN ijassa-713 50 6 . . PUNCT ijassa-713 51 1 ( ( PUNCT ijassa-713 51 2 2019 2019 NUM ijassa-713 51 3 ) ) PUNCT ijassa-713 51 4 are be AUX ijassa-713 51 5 independent independent ADJ ijassa-713 51 6 uncertain uncertain ADJ ijassa-713 51 7 variables variable NOUN ijassa-713 51 8 where where SCONJ ijassa-713 51 9 𝑑1 𝑑1 NOUN ijassa-713 51 10 , , PUNCT ijassa-713 51 11 𝑑2 𝑑2 PROPN ijassa-713 51 12 , , PUNCT ijassa-713 51 13 β‹― β‹― PROPN ijassa-713 51 14 , , PUNCT ijassa-713 51 15 π‘‘π‘˜ π‘‘π‘˜ ADV ijassa-713 51 16 are be AUX ijassa-713 51 17 any any DET ijassa-713 51 18 times time NOUN ijassa-713 51 19 with with ADP ijassa-713 51 20 𝑑0 𝑑0 PROPN ijassa-713 51 21 < < X ijassa-713 51 22 𝑑1 𝑑1 PROPN ijassa-713 51 23 < < X ijassa-713 51 24 β‹― β‹― X ijassa-713 51 25 < < X ijassa-713 51 26 π‘‘π‘˜ π‘‘π‘˜ PROPN ijassa-713 51 27 that that ADV ijassa-713 51 28 is is ADV ijassa-713 51 29 , , PUNCT ijassa-713 51 30 an an DET ijassa-713 51 31 independent independent ADJ ijassa-713 51 32 increment increment NOUN ijassa-713 51 33 process process NOUN ijassa-713 51 34 means mean VERB ijassa-713 51 35 that that SCONJ ijassa-713 51 36 its its PRON ijassa-713 51 37 increments increment NOUN ijassa-713 51 38 are be AUX ijassa-713 51 39 independent independent ADJ ijassa-713 51 40 uncertain uncertain ADJ ijassa-713 51 41 variables variable NOUN ijassa-713 51 42 whenever whenever SCONJ ijassa-713 51 43 the the DET ijassa-713 51 44 time time NOUN ijassa-713 51 45 intervals interval NOUN ijassa-713 51 46 do do AUX ijassa-713 51 47 not not PART ijassa-713 51 48 overlap overlap VERB ijassa-713 51 49 . . PUNCT ijassa-713 52 1 it it PRON ijassa-713 52 2 is be AUX ijassa-713 52 3 noted note VERB ijassa-713 52 4 that that SCONJ ijassa-713 52 5 the the DET ijassa-713 52 6 increments increment NOUN ijassa-713 52 7 are be AUX ijassa-713 52 8 also also ADV ijassa-713 52 9 independent independent ADJ ijassa-713 52 10 of of ADP ijassa-713 52 11 the the DET ijassa-713 52 12 initial initial ADJ ijassa-713 52 13 state state NOUN ijassa-713 52 14 . . PUNCT ijassa-713 53 1 definition definition NOUN ijassa-713 53 2 2.5 2.5 NUM ijassa-713 54 1 [ [ X ijassa-713 54 2 9 9 NUM ijassa-713 54 3 ] ] PUNCT ijassa-713 54 4 : : PUNCT ijassa-713 54 5 suppose suppose VERB ijassa-713 54 6 𝐢𝑑 𝐢𝑑 PROPN ijassa-713 54 7 is be AUX ijassa-713 54 8 a a DET ijassa-713 54 9 canonical canonical ADJ ijassa-713 54 10 liu liu NOUN ijassa-713 54 11 process process NOUN ijassa-713 54 12 , , PUNCT ijassa-713 54 13 and and CCONJ ijassa-713 54 14 𝑓 𝑓 X ijassa-713 54 15 and and CCONJ ijassa-713 54 16 𝑔 𝑔 PROPN ijassa-713 54 17 are be AUX ijassa-713 54 18 two two NUM ijassa-713 54 19 functions function NOUN ijassa-713 54 20 . . PUNCT ijassa-713 55 1 then then ADV ijassa-713 55 2 𝑑𝑋𝑑 𝑑𝑋𝑑 NOUN ijassa-713 55 3 = = SYM ijassa-713 55 4 𝑓(𝑑 𝑓(𝑑 NOUN ijassa-713 55 5 , , PUNCT ijassa-713 55 6 𝑋𝑑)𝑑𝑑 𝑋𝑑)𝑑𝑑 PROPN ijassa-713 55 7 + + CCONJ ijassa-713 55 8 𝑔(𝑑 𝑔(𝑑 PROPN ijassa-713 55 9 , , PUNCT ijassa-713 55 10 𝑋𝑑)𝑑𝐢𝑑 𝑋𝑑)𝑑𝐢𝑑 NOUN ijassa-713 55 11 ( ( PUNCT ijassa-713 55 12 2.6 2.6 NUM ijassa-713 55 13 ) ) PUNCT ijassa-713 55 14 is be AUX ijassa-713 55 15 called call VERB ijassa-713 55 16 an an DET ijassa-713 55 17 uncertain uncertain ADJ ijassa-713 55 18 differential differential NOUN ijassa-713 55 19 equation equation NOUN ijassa-713 55 20 . . PUNCT ijassa-713 56 1 a a DET ijassa-713 56 2 solution solution NOUN ijassa-713 56 3 is be AUX ijassa-713 56 4 a a DET ijassa-713 56 5 liu liu PROPN ijassa-713 56 6 process process NOUN ijassa-713 56 7 𝑋𝑑 𝑋𝑑 PROPN ijassa-713 56 8 that that PRON ijassa-713 56 9 satisfies satisfy VERB ijassa-713 56 10 ( ( PUNCT ijassa-713 56 11 2.3 2.3 NUM ijassa-713 56 12 ) ) PUNCT ijassa-713 56 13 and and CCONJ ijassa-713 56 14 ( ( PUNCT ijassa-713 56 15 2.4 2.4 NUM ijassa-713 56 16 ) ) PUNCT ijassa-713 56 17 identically identically ADV ijassa-713 56 18 in in ADP ijassa-713 56 19 𝑑. 𝑑. NOUN ijassa-713 56 20 definition definition NOUN ijassa-713 56 21 2.6 2.6 NUM ijassa-713 57 1 [ [ X ijassa-713 57 2 9 9 NUM ijassa-713 57 3 ] ] PUNCT ijassa-713 57 4 : : PUNCT ijassa-713 57 5 let let VERB ijassa-713 57 6 𝑋𝑑 𝑋𝑑 PRON ijassa-713 57 7 be be AUX ijassa-713 57 8 an an DET ijassa-713 57 9 uncertain uncertain ADJ ijassa-713 57 10 process process NOUN ijassa-713 57 11 . . PUNCT ijassa-713 58 1 then then ADV ijassa-713 58 2 for for ADP ijassa-713 58 3 each each DET ijassa-713 58 4 𝛾 𝛾 ADP ijassa-713 58 5 ∈ ∈ PROPN ijassa-713 58 6 𝛀 𝛀 PROPN ijassa-713 58 7 , , PUNCT ijassa-713 58 8 the the DET ijassa-713 58 9 function function NOUN ijassa-713 58 10 𝑋𝑑(𝛾)is 𝑋𝑑(𝛾)is PUNCT ijassa-713 58 11 called call VERB ijassa-713 58 12 a a DET ijassa-713 58 13 sample sample NOUN ijassa-713 58 14 path path NOUN ijassa-713 58 15 of of ADP ijassa-713 58 16 𝑋𝑑. 𝑋𝑑. PROPN ijassa-713 58 17 definition definition NOUN ijassa-713 58 18 2.7 2.7 NUM ijassa-713 58 19 [ [ X ijassa-713 58 20 11 11 NUM ijassa-713 58 21 ] ] X ijassa-713 58 22 : : PUNCT ijassa-713 58 23 an an DET ijassa-713 58 24 uncertain uncertain ADJ ijassa-713 58 25 process process NOUN ijassa-713 58 26 𝑋𝑑 𝑋𝑑 PROPN ijassa-713 58 27 is be AUX ijassa-713 58 28 said say VERB ijassa-713 58 29 to to PART ijassa-713 58 30 be be AUX ijassa-713 58 31 sample sample NOUN ijassa-713 58 32 - - PUNCT ijassa-713 58 33 continuous continuous ADJ ijassa-713 58 34 if if SCONJ ijassa-713 58 35 almost almost ADV ijassa-713 58 36 all all PRON ijassa-713 58 37 sample sample NOUN ijassa-713 58 38 paths path NOUN ijassa-713 58 39 are be AUX ijassa-713 58 40 continuous continuous ADJ ijassa-713 58 41 functions function NOUN ijassa-713 58 42 with with ADP ijassa-713 58 43 respect respect NOUN ijassa-713 58 44 to to ADP ijassa-713 58 45 time time NOUN ijassa-713 58 46 𝑑. 𝑑. NOUN ijassa-713 58 47 definition definition NOUN ijassa-713 58 48 2.8 2.8 NUM ijassa-713 58 49 uncertainty uncertainty NOUN ijassa-713 58 50 distribution distribution NOUN ijassa-713 58 51 of of ADP ijassa-713 58 52 solution solution NOUN ijassa-713 58 53 [ [ X ijassa-713 58 54 16 16 NUM ijassa-713 58 55 ] ] X ijassa-713 58 56 : : PUNCT ijassa-713 58 57 let let VERB ijassa-713 58 58 𝛼 𝛼 PRON ijassa-713 58 59 be be AUX ijassa-713 58 60 a a DET ijassa-713 58 61 number number NOUN ijassa-713 58 62 with with ADP ijassa-713 58 63 0 0 NUM ijassa-713 58 64 < < X ijassa-713 58 65 𝛼 𝛼 X ijassa-713 58 66 < < X ijassa-713 58 67 1 1 NUM ijassa-713 58 68 . . PUNCT ijassa-713 59 1 an an DET ijassa-713 59 2 uncertain uncertain ADJ ijassa-713 59 3 differential differential NOUN ijassa-713 59 4 equation equation NOUN ijassa-713 59 5 𝑑𝑋(𝑑 𝑑𝑋(𝑑 NOUN ijassa-713 59 6 ) ) PUNCT ijassa-713 60 1 = = PUNCT ijassa-713 60 2 𝑓(𝑑 𝑓(𝑑 NOUN ijassa-713 60 3 , , PUNCT ijassa-713 60 4 𝑋(𝑑))𝑑𝑑 𝑋(𝑑))𝑑𝑑 PROPN ijassa-713 60 5 + + PROPN ijassa-713 60 6 𝑔(𝑑 𝑔(𝑑 PROPN ijassa-713 60 7 , , PUNCT ijassa-713 60 8 𝑋(𝑑))𝑑𝐢(𝑑 𝑋(𝑑))𝑑𝐢(𝑑 NOUN ijassa-713 60 9 ) ) PUNCT ijassa-713 60 10 is be AUX ijassa-713 60 11 said say VERB ijassa-713 60 12 to to PART ijassa-713 60 13 have have VERB ijassa-713 60 14 an an DET ijassa-713 60 15 𝛼-path 𝛼-path NOUN ijassa-713 60 16 𝑋(𝑑)𝛼 𝑋(𝑑)𝛼 ADJ ijassa-713 60 17 if if SCONJ ijassa-713 60 18 it it PRON ijassa-713 60 19 solves solve VERB ijassa-713 60 20 the the DET ijassa-713 60 21 corresponding corresponding ADJ ijassa-713 60 22 ordinary ordinary ADJ ijassa-713 60 23 differential differential ADJ ijassa-713 60 24 equation equation NOUN ijassa-713 60 25 𝑑𝑋(𝑑)𝛼 𝑑𝑋(𝑑)𝛼 ADV ijassa-713 60 26 = = PUNCT ijassa-713 61 1 𝑓(𝑑 𝑓(𝑑 NOUN ijassa-713 61 2 , , PUNCT ijassa-713 61 3 𝑋(𝑑)𝛼)𝑑𝑑 𝑋(𝑑)𝛼)𝑑𝑑 PROPN ijassa-713 61 4 + + CCONJ ijassa-713 61 5 |𝑔(𝑑 |𝑔(𝑑 NOUN ijassa-713 61 6 , , PUNCT ijassa-713 61 7 𝑋(𝑑))|Ο†βˆ’1(𝛼)𝑑𝑑 𝑋(𝑑))|Ο†βˆ’1(𝛼)𝑑𝑑 NOUN ijassa-713 61 8 ( ( PUNCT ijassa-713 61 9 2.7 2.7 NUM ijassa-713 61 10 ) ) PUNCT ijassa-713 61 11 where where SCONJ ijassa-713 61 12 π›·βˆ’1(𝛼 π›·βˆ’1(𝛼 NOUN ijassa-713 61 13 ) ) PUNCT ijassa-713 61 14 is be AUX ijassa-713 61 15 the the DET ijassa-713 61 16 inverse inverse ADJ ijassa-713 61 17 uncertainty uncertainty NOUN ijassa-713 61 18 distribution distribution NOUN ijassa-713 61 19 of of ADP ijassa-713 61 20 standard standard ADJ ijassa-713 61 21 normal normal ADJ ijassa-713 61 22 uncertain uncertain ADJ ijassa-713 61 23 variable variable NOUN ijassa-713 61 24 , , PUNCT ijassa-713 61 25 that that ADV ijassa-713 61 26 is is ADV ijassa-713 61 27 , , PUNCT ijassa-713 61 28 Ο†βˆ’1(𝛼 Ο†βˆ’1(𝛼 NOUN ijassa-713 61 29 ) ) PUNCT ijassa-713 61 30 = = SYM ijassa-713 62 1 √3 √3 NOUN ijassa-713 62 2 πœ‹ πœ‹ NOUN ijassa-713 62 3 ln ln NOUN ijassa-713 62 4 𝛼 𝛼 PROPN ijassa-713 62 5 1 1 NUM ijassa-713 62 6 βˆ’ βˆ’ PROPN ijassa-713 62 7 𝛼 𝛼 NOUN ijassa-713 62 8 , , PUNCT ijassa-713 62 9 𝛼 𝛼 PROPN ijassa-713 62 10 ∈ ∈ PROPN ijassa-713 62 11 β„œ β„œ PROPN ijassa-713 62 12 theorem theorem VERB ijassa-713 62 13 2.1 2.1 NUM ijassa-713 62 14 extreme extreme ADJ ijassa-713 62 15 value value NOUN ijassa-713 62 16 of of ADP ijassa-713 62 17 solution solution NOUN ijassa-713 62 18 [ [ X ijassa-713 62 19 18 18 NUM ijassa-713 62 20 ] ] X ijassa-713 62 21 : : PUNCT ijassa-713 62 22 let let VERB ijassa-713 62 23 𝑋(𝑑 𝑋(𝑑 NUM ijassa-713 62 24 ) ) PUNCT ijassa-713 62 25 and and CCONJ ijassa-713 62 26 𝑋(𝑑)𝛼 𝑋(𝑑)𝛼 PROPN ijassa-713 62 27 be be VERB ijassa-713 62 28 the the DET ijassa-713 62 29 solution solution NOUN ijassa-713 62 30 and and CCONJ ijassa-713 62 31 𝛼-path 𝛼-path NOUN ijassa-713 62 32 of of ADP ijassa-713 62 33 the the DET ijassa-713 62 34 uncertain uncertain ADJ ijassa-713 62 35 differential differential ADJ ijassa-713 62 36 equation equation NOUN ijassa-713 62 37 ( ( PUNCT ijassa-713 62 38 2.6 2.6 NUM ijassa-713 62 39 ) ) PUNCT ijassa-713 62 40 . . PUNCT ijassa-713 63 1 then then ADV ijassa-713 63 2 , , PUNCT ijassa-713 63 3 for for ADP ijassa-713 63 4 any any DET ijassa-713 63 5 time time NOUN ijassa-713 63 6 𝑑 𝑑 X ijassa-713 63 7 > > X ijassa-713 63 8 0 0 PUNCT ijassa-713 63 9 and and CCONJ ijassa-713 63 10 strictly strictly ADV ijassa-713 63 11 increasing increase VERB ijassa-713 63 12 function function NOUN ijassa-713 63 13 𝐽(π‘₯ 𝐽(π‘₯ NUM ijassa-713 63 14 ) ) PUNCT ijassa-713 63 15 , , PUNCT ijassa-713 63 16 the the DET ijassa-713 63 17 supremum supremum ADJ ijassa-713 63 18 sup𝑑0≀𝑑≀𝑑𝑛 sup𝑑0≀𝑑≀𝑑𝑛 NOUN ijassa-713 63 19 𝐽(𝑋(𝑑 𝐽(𝑋(𝑑 PRON ijassa-713 63 20 ) ) PUNCT ijassa-713 63 21 ) ) PUNCT ijassa-713 63 22 has have VERB ijassa-713 63 23 an an DET ijassa-713 63 24 inverse inverse ADJ ijassa-713 63 25 uncertainty uncertainty NOUN ijassa-713 63 26 distribution distribution NOUN ijassa-713 63 27 Οˆβˆ’1(𝛼 Οˆβˆ’1(𝛼 NOUN ijassa-713 63 28 ) ) PUNCT ijassa-713 63 29 = = SYM ijassa-713 63 30 sup𝑑0≀𝑑≀𝑑𝑛 sup𝑑0≀𝑑≀𝑑𝑛 PROPN ijassa-713 63 31 𝐽(𝑋(𝑑)𝛼 𝐽(𝑋(𝑑)𝛼 NUM ijassa-713 63 32 ) ) PUNCT ijassa-713 63 33 ( ( PUNCT ijassa-713 63 34 2.8 2.8 NUM ijassa-713 63 35 ) ) PUNCT ijassa-713 63 36 and and CCONJ ijassa-713 63 37 the the DET ijassa-713 63 38 infimum infimum ADJ ijassa-713 63 39 inf𝑑0≀𝑑≀𝑑𝑛 inf𝑑0≀𝑑≀𝑑𝑛 PROPN ijassa-713 63 40 𝐽(𝑋(𝑑 𝐽(𝑋(𝑑 PRON ijassa-713 63 41 ) ) PUNCT ijassa-713 63 42 ) ) PUNCT ijassa-713 63 43 has have VERB ijassa-713 63 44 an an DET ijassa-713 63 45 inverse inverse ADJ ijassa-713 63 46 uncertainty uncertainty NOUN ijassa-713 63 47 distribution distribution NOUN ijassa-713 63 48 Οˆβˆ’1(𝛼 Οˆβˆ’1(𝛼 NOUN ijassa-713 63 49 ) ) PUNCT ijassa-713 63 50 = = SYM ijassa-713 64 1 inf𝑑0≀𝑑≀𝑑𝑛 inf𝑑0≀𝑑≀𝑑𝑛 PROPN ijassa-713 64 2 𝐽(𝑋(𝑑)𝛼 𝐽(𝑋(𝑑)𝛼 NUM ijassa-713 64 3 ) ) PUNCT ijassa-713 64 4 ( ( PUNCT ijassa-713 64 5 2.9 2.9 NUM ijassa-713 64 6 ) ) PUNCT ijassa-713 64 7 theorem theorem VERB ijassa-713 64 8 2.2 2.2 NUM ijassa-713 65 1 [ [ X ijassa-713 65 2 16 16 NUM ijassa-713 65 3 ] ] X ijassa-713 65 4 : : PUNCT ijassa-713 65 5 let let VERB ijassa-713 65 6 𝑋(𝑑 𝑋(𝑑 NUM ijassa-713 65 7 ) ) PUNCT ijassa-713 65 8 and and CCONJ ijassa-713 65 9 𝑋(𝑑)𝛼 𝑋(𝑑)𝛼 PROPN ijassa-713 65 10 be be VERB ijassa-713 65 11 the the DET ijassa-713 65 12 solution solution NOUN ijassa-713 65 13 and and CCONJ ijassa-713 65 14 𝛼-path 𝛼-path NOUN ijassa-713 65 15 of of ADP ijassa-713 65 16 the the DET ijassa-713 65 17 uncertain uncertain ADJ ijassa-713 65 18 differential differential ADJ ijassa-713 65 19 equation equation NOUN ijassa-713 65 20 ( ( PUNCT ijassa-713 65 21 2.6 2.6 NUM ijassa-713 65 22 ) ) PUNCT ijassa-713 65 23 . . PUNCT ijassa-713 66 1 then then ADV ijassa-713 66 2 𝑀{𝑋(𝑑 𝑀{𝑋(𝑑 X ijassa-713 66 3 ) ) PUNCT ijassa-713 66 4 ≀ ≀ NOUN ijassa-713 66 5 𝑋(𝑑)𝛼 𝑋(𝑑)𝛼 ADJ ijassa-713 66 6 , , PUNCT ijassa-713 66 7 βˆ€π‘‘ βˆ€π‘‘ PROPN ijassa-713 66 8 } } PUNCT ijassa-713 66 9 = = SYM ijassa-713 66 10 𝛼 𝛼 X ijassa-713 66 11 , , PUNCT ijassa-713 66 12 𝑀{𝑋(𝑑 𝑀{𝑋(𝑑 NOUN ijassa-713 66 13 ) ) PUNCT ijassa-713 66 14 > > X ijassa-713 67 1 𝑋(𝑑)𝛼 𝑋(𝑑)𝛼 PROPN ijassa-713 67 2 , , PUNCT ijassa-713 67 3 βˆ€π‘‘ βˆ€π‘‘ PROPN ijassa-713 67 4 } } PUNCT ijassa-713 67 5 = = SYM ijassa-713 67 6 1 1 NUM ijassa-713 67 7 βˆ’ βˆ’ PROPN ijassa-713 67 8 𝛼. 𝛼. NOUN ijassa-713 67 9 ( ( PUNCT ijassa-713 67 10 2.10 2.10 NUM ijassa-713 67 11 ) ) PUNCT ijassa-713 67 12 3 3 NUM ijassa-713 67 13 . . PUNCT ijassa-713 67 14 model model NOUN ijassa-713 67 15 formulation formulation NOUN ijassa-713 67 16 a a DET ijassa-713 67 17 model model NOUN ijassa-713 67 18 of of ADP ijassa-713 67 19 capital capital NOUN ijassa-713 67 20 asset asset NOUN ijassa-713 67 21 management management NOUN ijassa-713 67 22 is be AUX ijassa-713 67 23 presented present VERB ijassa-713 67 24 herein herein NOUN ijassa-713 67 25 such such ADJ ijassa-713 67 26 that that SCONJ ijassa-713 67 27 it it PRON ijassa-713 67 28 is be AUX ijassa-713 67 29 assumed assume VERB ijassa-713 67 30 that that SCONJ ijassa-713 67 31 an an DET ijassa-713 67 32 investor investor NOUN ijassa-713 67 33 invests invest VERB ijassa-713 67 34 his his PRON ijassa-713 67 35 wealth wealth NOUN ijassa-713 67 36 in in ADP ijassa-713 67 37 capital capital NOUN ijassa-713 67 38 asset asset NOUN ijassa-713 67 39 , , PUNCT ijassa-713 67 40 𝐴(𝑑 𝐴(𝑑 PROPN ijassa-713 67 41 ) ) PUNCT ijassa-713 67 42 , , PUNCT ijassa-713 67 43 of of ADP ijassa-713 67 44 a a DET ijassa-713 67 45 large large ADJ ijassa-713 67 46 business business NOUN ijassa-713 67 47 for for ADP ijassa-713 67 48 time time NOUN ijassa-713 67 49 , , PUNCT ijassa-713 67 50 𝑑 𝑑 PROPN ijassa-713 67 51 , , PUNCT ijassa-713 67 52 from from ADP ijassa-713 67 53 𝑑0 𝑑0 PROPN ijassa-713 67 54 to to AUX ijassa-713 67 55 𝑑𝑓. 𝑑𝑓. VERB ijassa-713 67 56 t. t. PROPN ijassa-713 67 57 latunde latunde VERB ijassa-713 67 58 55 55 NUM ijassa-713 67 59 copyright copyright NOUN ijassa-713 67 60 Β© Β© PROPN ijassa-713 67 61 2019 2019 NUM ijassa-713 67 62 assa assa NOUN ijassa-713 67 63 . . PUNCT ijassa-713 68 1 adv adv PROPN ijassa-713 68 2 . . PUNCT ijassa-713 69 1 in in ADP ijassa-713 69 2 systems system NOUN ijassa-713 69 3 science science NOUN ijassa-713 69 4 and and CCONJ ijassa-713 69 5 appl appl NOUN ijassa-713 69 6 . . PUNCT ijassa-713 70 1 ( ( PUNCT ijassa-713 70 2 2019 2019 NUM ijassa-713 70 3 ) ) PUNCT ijassa-713 70 4 suppose suppose VERB ijassa-713 70 5 he he PRON ijassa-713 70 6 starts start VERB ijassa-713 70 7 with with ADP ijassa-713 70 8 a a DET ijassa-713 70 9 known know VERB ijassa-713 70 10 initial initial ADJ ijassa-713 70 11 net net ADJ ijassa-713 70 12 worth worth NOUN ijassa-713 70 13 𝑋0(𝑑 𝑋0(𝑑 NUM ijassa-713 70 14 ) ) PUNCT ijassa-713 70 15 . . PUNCT ijassa-713 71 1 at at ADP ijassa-713 71 2 time time NOUN ijassa-713 71 3 𝑑 𝑑 PROPN ijassa-713 71 4 , , PUNCT ijassa-713 71 5 what what DET ijassa-713 71 6 ratio ratio NOUN ijassa-713 71 7 of of ADP ijassa-713 71 8 his his PRON ijassa-713 71 9 net net ADJ ijassa-713 71 10 worth worth NOUN ijassa-713 71 11 , , PUNCT ijassa-713 71 12 πœ“ πœ“ NOUN ijassa-713 71 13 , , PUNCT ijassa-713 71 14 must must AUX ijassa-713 71 15 he he PRON ijassa-713 71 16 select select VERB ijassa-713 71 17 to to PART ijassa-713 71 18 utilize utilize VERB ijassa-713 71 19 on on ADP ijassa-713 71 20 capital capital NOUN ijassa-713 71 21 asset asset NOUN ijassa-713 71 22 in in ADP ijassa-713 71 23 the the DET ijassa-713 71 24 presence presence NOUN ijassa-713 71 25 of of ADP ijassa-713 71 26 liability liability NOUN ijassa-713 71 27 such such ADJ ijassa-713 71 28 that that SCONJ ijassa-713 71 29 the the DET ijassa-713 71 30 expected expect VERB ijassa-713 71 31 net net ADJ ijassa-713 71 32 present present ADJ ijassa-713 71 33 value value NOUN ijassa-713 71 34 of of ADP ijassa-713 71 35 the the DET ijassa-713 71 36 utility utility NOUN ijassa-713 71 37 of of ADP ijassa-713 71 38 asset asset NOUN ijassa-713 71 39 , , PUNCT ijassa-713 71 40 𝐽(πœ“ 𝐽(πœ“ PROPN ijassa-713 71 41 ) ) PUNCT ijassa-713 71 42 , , PUNCT ijassa-713 71 43 is be AUX ijassa-713 71 44 optimized optimize VERB ijassa-713 71 45 ? ? PUNCT ijassa-713 72 1 table table NOUN ijassa-713 72 2 3.1 3.1 NUM ijassa-713 72 3 . . PUNCT ijassa-713 73 1 definition definition NOUN ijassa-713 73 2 of of ADP ijassa-713 73 3 parameters parameter NOUN ijassa-713 73 4 of of ADP ijassa-713 73 5 the the DET ijassa-713 73 6 objective objective ADJ ijassa-713 73 7 function function NOUN ijassa-713 73 8 to to ADP ijassa-713 73 9 the the DET ijassa-713 73 10 model model NOUN ijassa-713 73 11 parameter parameter NOUN ijassa-713 73 12 description description NOUN ijassa-713 73 13 π‘ˆ π‘ˆ PROPN ijassa-713 73 14 utility utility NOUN ijassa-713 73 15 function function NOUN ijassa-713 73 16 𝐴(𝑑 𝐴(𝑑 NOUN ijassa-713 73 17 ) ) PUNCT ijassa-713 73 18 capital capital NOUN ijassa-713 73 19 asset asset NOUN ijassa-713 73 20 at at ADP ijassa-713 73 21 time time NOUN ijassa-713 73 22 𝑑 𝑑 ADP ijassa-713 73 23 πœ‚ πœ‚ DET ijassa-713 73 24 subjective subjective ADJ ijassa-713 73 25 discount discount NOUN ijassa-713 73 26 rate rate NOUN ijassa-713 73 27 , , PUNCT ijassa-713 73 28 e.g. e.g. ADV ijassa-713 73 29 , , PUNCT ijassa-713 73 30 𝐴 𝐴 PROPN ijassa-713 73 31 πœ‚+1 πœ‚+1 X ijassa-713 73 32 = = SYM ijassa-713 73 33 presentvalue presentvalue PROPN ijassa-713 73 34 πœ† πœ† DET ijassa-713 73 35 degree degree NOUN ijassa-713 73 36 of of ADP ijassa-713 73 37 relative relative ADJ ijassa-713 73 38 risk risk NOUN ijassa-713 73 39 , , PUNCT ijassa-713 73 40 where where SCONJ ijassa-713 73 41 ( ( PUNCT ijassa-713 73 42 1 1 NUM ijassa-713 73 43 βˆ’ βˆ’ NOUN ijassa-713 73 44 πœ† πœ† NOUN ijassa-713 73 45 ) ) PUNCT ijassa-713 73 46 is be AUX ijassa-713 73 47 the the DET ijassa-713 73 48 risk risk NOUN ijassa-713 73 49 aversion aversion NOUN ijassa-713 73 50 πœ“ πœ“ ADP ijassa-713 73 51 capital capital NOUN ijassa-713 73 52 asset asset NOUN ijassa-713 73 53 ratio ratio NOUN ijassa-713 73 54 ( ( PUNCT ijassa-713 73 55 control control NOUN ijassa-713 73 56 ) ) PUNCT ijassa-713 73 57 πœ“ πœ“ PROPN ijassa-713 73 58 ∈ ∈ PROPN ijassa-713 73 59 β„œ β„œ PROPN ijassa-713 73 60 𝑋(𝑑 𝑋(𝑑 PROPN ijassa-713 73 61 ) ) PUNCT ijassa-713 73 62 net net ADJ ijassa-713 73 63 worth worth NOUN ijassa-713 73 64 at at ADP ijassa-713 73 65 time time NOUN ijassa-713 73 66 ( ( PUNCT ijassa-713 73 67 state state NOUN ijassa-713 73 68 variable)𝑑 variable)𝑑 PROPN ijassa-713 73 69 table table NOUN ijassa-713 73 70 3.2 3.2 NUM ijassa-713 73 71 : : PUNCT ijassa-713 73 72 definition definition NOUN ijassa-713 73 73 of of ADP ijassa-713 73 74 parameters parameter NOUN ijassa-713 73 75 of of ADP ijassa-713 73 76 the the DET ijassa-713 73 77 constraint constraint NOUN ijassa-713 73 78 to to ADP ijassa-713 73 79 the the DET ijassa-713 73 80 model model NOUN ijassa-713 73 81 parameter parameter NOUN ijassa-713 73 82 description description NOUN ijassa-713 73 83 πœŽπ‘Ÿ(𝑑 πœŽπ‘Ÿ(𝑑 NOUN ijassa-713 73 84 ) ) PUNCT ijassa-713 73 85 diffusion diffusion NOUN ijassa-713 73 86 volatility volatility NOUN ijassa-713 73 87 of of ADP ijassa-713 73 88 liability liability NOUN ijassa-713 73 89 ( ( PUNCT ijassa-713 73 90 with with ADP ijassa-713 73 91 variance variance NOUN ijassa-713 73 92 πœŽπ‘Ÿ πœŽπ‘Ÿ ADP ijassa-713 73 93 2 2 NUM ijassa-713 73 94 per per ADP ijassa-713 73 95 unit unit NOUN ijassa-713 73 96 time time NOUN ijassa-713 73 97 ) ) PUNCT ijassa-713 73 98 πœ“ πœ“ PROPN ijassa-713 73 99 capital capital NOUN ijassa-713 73 100 asset asset NOUN ijassa-713 73 101 ratio ratio NOUN ijassa-713 73 102 ( ( PUNCT ijassa-713 73 103 control control NOUN ijassa-713 73 104 ) ) PUNCT ijassa-713 73 105 πœ“ πœ“ PROPN ijassa-713 73 106 ∈ ∈ PROPN ijassa-713 73 107 β„œ β„œ PROPN ijassa-713 73 108 πœŽπ‘(𝑑 πœŽπ‘(𝑑 NOUN ijassa-713 73 109 ) ) PUNCT ijassa-713 73 110 diffusion diffusion NOUN ijassa-713 73 111 volatility volatility NOUN ijassa-713 73 112 of of ADP ijassa-713 73 113 asset asset NOUN ijassa-713 73 114 ( ( PUNCT ijassa-713 73 115 with with ADP ijassa-713 73 116 variance variance NOUN ijassa-713 73 117 πœŽπ‘ πœŽπ‘ PROPN ijassa-713 73 118 2 2 NUM ijassa-713 73 119 per per ADP ijassa-713 73 120 unit unit NOUN ijassa-713 73 121 time time NOUN ijassa-713 73 122 ) ) PUNCT ijassa-713 73 123 πœ…(𝑑 πœ…(𝑑 ADJ ijassa-713 73 124 ) ) PUNCT ijassa-713 73 125 capital capital NOUN ijassa-713 73 126 gain gain NOUN ijassa-713 73 127 on on ADP ijassa-713 73 128 asset asset NOUN ijassa-713 73 129 due due ADP ijassa-713 73 130 to to ADP ijassa-713 73 131 inflation inflation NOUN ijassa-713 73 132 at at ADP ijassa-713 73 133 time time NOUN ijassa-713 73 134 𝑑 𝑑 PROPN ijassa-713 73 135 πœŽπ‘(𝑑 πœŽπ‘(𝑑 NUM ijassa-713 73 136 ) ) PUNCT ijassa-713 73 137 diffusion diffusion NOUN ijassa-713 73 138 volatility volatility NOUN ijassa-713 73 139 on on ADP ijassa-713 73 140 asset asset NOUN ijassa-713 73 141 price price NOUN ijassa-713 73 142 ( ( PUNCT ijassa-713 73 143 with with ADP ijassa-713 73 144 variance variance NOUN ijassa-713 73 145 πœŽπ‘ πœŽπ‘ ADP ijassa-713 73 146 2 2 NUM ijassa-713 73 147 per per ADP ijassa-713 73 148 unit unit NOUN ijassa-713 73 149 time time NOUN ijassa-713 73 150 ) ) PUNCT ijassa-713 73 151 𝛽(𝑑 𝛽(𝑑 PROPN ijassa-713 73 152 ) ) PUNCT ijassa-713 73 153 mean mean VERB ijassa-713 73 154 rate rate NOUN ijassa-713 73 155 of of ADP ijassa-713 73 156 return return NOUN ijassa-713 73 157 on on ADP ijassa-713 73 158 asset asset NOUN ijassa-713 73 159 πœ” πœ” PROPN ijassa-713 73 160 mean mean NOUN ijassa-713 73 161 interest interest NOUN ijassa-713 73 162 rate rate NOUN ijassa-713 73 163 of of ADP ijassa-713 73 164 liability liability NOUN ijassa-713 73 165 𝐢(𝑑 𝐢(𝑑 NOUN ijassa-713 73 166 ) ) PUNCT ijassa-713 73 167 uncertain uncertain ADJ ijassa-713 73 168 process process NOUN ijassa-713 73 169 at at ADP ijassa-713 73 170 time time NOUN ijassa-713 73 171 𝑑 𝑑 ADP ijassa-713 73 172 πœ‡(𝑑 πœ‡(𝑑 NOUN ijassa-713 73 173 ) ) PUNCT ijassa-713 73 174 consumption consumption NOUN ijassa-713 73 175 level level NOUN ijassa-713 73 176 at at ADP ijassa-713 73 177 time time NOUN ijassa-713 73 178 𝑑 𝑑 PROPN ijassa-713 73 179 𝑗(𝑑 𝑗(𝑑 PROPN ijassa-713 73 180 ) ) PUNCT ijassa-713 73 181 tax tax NOUN ijassa-713 73 182 ratio ratio NOUN ijassa-713 73 183 at at ADP ijassa-713 73 184 time time NOUN ijassa-713 73 185 𝑑 𝑑 PROPN ijassa-713 73 186 𝑔(𝑑 𝑔(𝑑 PROPN ijassa-713 73 187 ) ) PUNCT ijassa-713 73 188 depreciation depreciation NOUN ijassa-713 73 189 ratio ratio NOUN ijassa-713 73 190 at at ADP ijassa-713 73 191 time time NOUN ijassa-713 73 192 𝑑 𝑑 PROPN ijassa-713 73 193 β„Ž(𝑑 β„Ž(𝑑 PROPN ijassa-713 73 194 ) ) PUNCT ijassa-713 73 195 asset asset NOUN ijassa-713 73 196 supplies supply VERB ijassa-713 73 197 ratio ratio NOUN ijassa-713 73 198 at at ADP ijassa-713 73 199 time time NOUN ijassa-713 73 200 𝑑 𝑑 PROPN ijassa-713 73 201 theorem theorem VERB ijassa-713 73 202 3.1 3.1 NUM ijassa-713 74 1 [ [ X ijassa-713 74 2 12 12 NUM ijassa-713 74 3 ] ] X ijassa-713 74 4 : : PUNCT ijassa-713 74 5 if if SCONJ ijassa-713 74 6 πœ† πœ† DET ijassa-713 74 7 > > X ijassa-713 74 8 0 0 PUNCT ijassa-713 74 9 and and CCONJ ijassa-713 74 10 π‘ˆ π‘ˆ PROPN ijassa-713 74 11 is be AUX ijassa-713 74 12 such such ADJ ijassa-713 74 13 that that SCONJ ijassa-713 74 14 the the DET ijassa-713 74 15 integral integral ADJ ijassa-713 74 16 𝐸𝐢 𝐸𝐢 NOUN ijassa-713 74 17 [ [ X ijassa-713 74 18 ∫ ∫ X ijassa-713 74 19 𝑑𝑓 𝑑𝑓 PROPN ijassa-713 74 20 𝑑0 𝑑0 PROPN ijassa-713 74 21 π‘ˆ(𝐴 π‘ˆ(𝐴 PROPN ijassa-713 74 22 , , PUNCT ijassa-713 74 23 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN ijassa-713 74 24 ] ] PUNCT ijassa-713 74 25 is be AUX ijassa-713 74 26 absolutely absolutely ADV ijassa-713 74 27 convergent convergent ADJ ijassa-713 74 28 , , PUNCT ijassa-713 74 29 then then ADV ijassa-713 74 30 the the DET ijassa-713 74 31 maximization maximization NOUN ijassa-713 74 32 or or CCONJ ijassa-713 74 33 minimization minimization NOUN ijassa-713 74 34 of of ADP ijassa-713 74 35 𝐸𝐢 𝐸𝐢 PROPN ijassa-713 74 36 [ [ X ijassa-713 74 37 ∫ ∫ X ijassa-713 74 38 𝑑𝑓 𝑑𝑓 PROPN ijassa-713 74 39 𝑑0 𝑑0 PROPN ijassa-713 74 40 π‘ˆ(𝐴 π‘ˆ(𝐴 PROPN ijassa-713 74 41 , , PUNCT ijassa-713 75 1 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN ijassa-713 75 2 ] ] PUNCT ijassa-713 75 3 is be AUX ijassa-713 75 4 equivalent equivalent ADJ ijassa-713 75 5 to to ADP ijassa-713 75 6 the the DET ijassa-713 75 7 maximization maximization NOUN ijassa-713 75 8 or or CCONJ ijassa-713 75 9 minimization minimization NOUN ijassa-713 75 10 of of ADP ijassa-713 75 11 𝐸0 𝐸0 PROPN ijassa-713 76 1 ∫ ∫ PROPN ijassa-713 76 2 𝑑𝑓 𝑑𝑓 PROPN ijassa-713 76 3 𝑑0 𝑑0 PROPN ijassa-713 76 4 π‘’βˆ’πœ‚π‘‘π‘ˆ(𝐴 π‘’βˆ’πœ‚π‘‘π‘ˆ(𝐴 PROPN ijassa-713 76 5 , , PUNCT ijassa-713 76 6 𝑑)𝑑𝑑 𝑑)𝑑𝑑 PROPN ijassa-713 76 7 where where SCONJ ijassa-713 76 8 𝐸𝐢 𝐸𝐢 PROPN ijassa-713 76 9 is be AUX ijassa-713 76 10 the the DET ijassa-713 76 11 conditional conditional ADJ ijassa-713 76 12 expectation expectation NOUN ijassa-713 76 13 operator operator NOUN ijassa-713 76 14 over over ADP ijassa-713 76 15 all all DET ijassa-713 76 16 random random ADJ ijassa-713 76 17 variables variable NOUN ijassa-713 76 18 excluding exclude VERB ijassa-713 76 19 πœ†. πœ†. NOUN ijassa-713 76 20 by by ADP ijassa-713 76 21 theorem theorem ADJ ijassa-713 76 22 3.1 3.1 NUM ijassa-713 76 23 , , PUNCT ijassa-713 76 24 an an DET ijassa-713 76 25 investor investor NOUN ijassa-713 76 26 who who PRON ijassa-713 76 27 faces face VERB ijassa-713 76 28 an an DET ijassa-713 76 29 exponentially exponentially ADV ijassa-713 76 30 - - PUNCT ijassa-713 76 31 distributed distribute VERB ijassa-713 76 32 uncertain uncertain ADJ ijassa-713 76 33 investment investment NOUN ijassa-713 76 34 of of ADP ijassa-713 76 35 capital capital NOUN ijassa-713 76 36 asset asset NOUN ijassa-713 76 37 invests invest NOUN ijassa-713 76 38 as as SCONJ ijassa-713 76 39 if if SCONJ ijassa-713 76 40 there there PRON ijassa-713 76 41 is be VERB ijassa-713 76 42 no no DET ijassa-713 76 43 terminal terminal ADJ ijassa-713 76 44 period period NOUN ijassa-713 76 45 , , PUNCT ijassa-713 76 46 but but CCONJ ijassa-713 76 47 with with ADP ijassa-713 76 48 a a DET ijassa-713 76 49 subjective subjective ADJ ijassa-713 76 50 rate rate NOUN ijassa-713 76 51 of of ADP ijassa-713 76 52 time time NOUN ijassa-713 76 53 preference preference NOUN ijassa-713 76 54 equal equal ADJ ijassa-713 76 55 to to ADP ijassa-713 76 56 the the DET ijassa-713 76 57 investments investment NOUN ijassa-713 76 58 terminals terminal NOUN ijassa-713 76 59 . . PUNCT ijassa-713 77 1 𝐽 𝐽 PROPN ijassa-713 77 2 = = PUNCT ijassa-713 77 3 opt𝐸𝐢 opt𝐸𝐢 PROPN ijassa-713 77 4 [ [ PUNCT ijassa-713 77 5 ∫ ∫ PROPN ijassa-713 77 6 𝑑𝑓 𝑑𝑓 NOUN ijassa-713 77 7 𝑑0 𝑑0 PROPN ijassa-713 77 8 π‘’βˆ’πœ‚π‘‘π‘ˆ(𝐴(𝑑))𝑑𝑑 π‘’βˆ’πœ‚π‘‘π‘ˆ(𝐴(𝑑))𝑑𝑑 PROPN ijassa-713 77 9 ] ] X ijassa-713 77 10 ( ( PUNCT ijassa-713 77 11 3.1 3.1 NUM ijassa-713 77 12 ) ) PUNCT ijassa-713 77 13 where where SCONJ ijassa-713 77 14 𝐸𝐢 𝐸𝐢 PROPN ijassa-713 77 15 denotes denote VERB ijassa-713 77 16 conditional conditional ADJ ijassa-713 77 17 expectation expectation NOUN ijassa-713 77 18 , , PUNCT ijassa-713 77 19 πœ‚ πœ‚ PROPN ijassa-713 77 20 ∈ ∈ PROPN ijassa-713 77 21 ( ( PUNCT ijassa-713 77 22 0,1 0,1 NOUN ijassa-713 77 23 ) ) PUNCT ijassa-713 77 24 is be AUX ijassa-713 77 25 the the DET ijassa-713 77 26 arbitrary arbitrary ADJ ijassa-713 77 27 discount discount NOUN ijassa-713 77 28 rate rate NOUN ijassa-713 77 29 . . PUNCT ijassa-713 78 1 in in ADP ijassa-713 78 2 selecting select VERB ijassa-713 78 3 the the DET ijassa-713 78 4 discount discount NOUN ijassa-713 78 5 rate rate NOUN ijassa-713 78 6 , , PUNCT ijassa-713 78 7 the the DET ijassa-713 78 8 effective effective ADJ ijassa-713 78 9 length length NOUN ijassa-713 78 10 of of ADP ijassa-713 78 11 time time NOUN ijassa-713 78 12 is be AUX ijassa-713 78 13 inversely inversely ADV ijassa-713 78 14 proportional proportional ADJ ijassa-713 78 15 to to ADP ijassa-713 78 16 the the DET ijassa-713 78 17 discount discount NOUN ijassa-713 78 18 rate rate NOUN ijassa-713 78 19 in in ADP ijassa-713 78 20 the the DET ijassa-713 78 21 sense sense NOUN ijassa-713 78 22 that that SCONJ ijassa-713 78 23 a a DET ijassa-713 78 24 high high ADJ ijassa-713 78 25 discount discount NOUN ijassa-713 78 26 rate rate NOUN ijassa-713 78 27 implies imply VERB ijassa-713 78 28 a a DET ijassa-713 78 29 short short ADJ ijassa-713 78 30 time time NOUN ijassa-713 78 31 interval interval NOUN ijassa-713 78 32 , , PUNCT ijassa-713 78 33 [ [ X ijassa-713 78 34 15 15 NUM ijassa-713 78 35 ] ] PUNCT ijassa-713 78 36 . . PUNCT ijassa-713 79 1 utility utility NOUN ijassa-713 79 2 function function NOUN ijassa-713 79 3 π‘ˆ(𝐴 π‘ˆ(𝐴 NOUN ijassa-713 79 4 ) ) PUNCT ijassa-713 79 5 measures measure NOUN ijassa-713 79 6 satisfaction satisfaction NOUN ijassa-713 79 7 of of ADP ijassa-713 79 8 an an DET ijassa-713 79 9 investor investor NOUN ijassa-713 79 10 as as ADP ijassa-713 79 11 a a DET ijassa-713 79 12 function function NOUN ijassa-713 79 13 of of ADP ijassa-713 79 14 usage usage NOUN ijassa-713 79 15 or or CCONJ ijassa-713 79 16 efficiency efficiency NOUN ijassa-713 79 17 of of ADP ijassa-713 79 18 capital capital NOUN ijassa-713 79 19 assets asset NOUN ijassa-713 79 20 with with ADP ijassa-713 79 21 respect respect NOUN ijassa-713 79 22 to to ADP ijassa-713 79 23 risk risk NOUN ijassa-713 79 24 aversion aversion NOUN ijassa-713 79 25 . . PUNCT ijassa-713 80 1 however however ADV ijassa-713 80 2 , , PUNCT ijassa-713 80 3 risk risk NOUN ijassa-713 80 4 aversion aversion NOUN ijassa-713 80 5 is be AUX ijassa-713 80 6 the the DET ijassa-713 80 7 behaviour behaviour NOUN ijassa-713 80 8 of of ADP ijassa-713 80 9 the the DET ijassa-713 80 10 investors investor NOUN ijassa-713 80 11 when when SCONJ ijassa-713 80 12 exposed expose VERB ijassa-713 80 13 56 56 NUM ijassa-713 80 14 optimal optimal ADJ ijassa-713 80 15 values value NOUN ijassa-713 80 16 in in ADP ijassa-713 80 17 uncertin uncertin PROPN ijassa-713 80 18 optimal optimal ADJ ijassa-713 80 19 control control NOUN ijassa-713 80 20 model model NOUN ijassa-713 80 21 copyright copyright NOUN ijassa-713 80 22 Β© Β© PROPN ijassa-713 80 23 2019 2019 NUM ijassa-713 80 24 assa assa PROPN ijassa-713 80 25 adv adv PROPN ijassa-713 80 26 . . PUNCT ijassa-713 81 1 in in ADP ijassa-713 81 2 systems system NOUN ijassa-713 81 3 science science NOUN ijassa-713 81 4 and and CCONJ ijassa-713 81 5 appl appl NOUN ijassa-713 81 6 . . PUNCT ijassa-713 82 1 ( ( PUNCT ijassa-713 82 2 2019 2019 NUM ijassa-713 82 3 ) ) PUNCT ijassa-713 82 4 to to PART ijassa-713 82 5 attempt attempt VERB ijassa-713 82 6 to to PART ijassa-713 82 7 reduce reduce VERB ijassa-713 82 8 the the DET ijassa-713 82 9 uncertainty uncertainty NOUN ijassa-713 82 10 in in ADP ijassa-713 82 11 their their PRON ijassa-713 82 12 investments investment NOUN ijassa-713 82 13 . . PUNCT ijassa-713 83 1 there there PRON ijassa-713 83 2 are be VERB ijassa-713 83 3 various various ADJ ijassa-713 83 4 measures measure NOUN ijassa-713 83 5 of of ADP ijassa-713 83 6 risk risk NOUN ijassa-713 83 7 aversion aversion NOUN ijassa-713 83 8 under under ADP ijassa-713 83 9 expected expect VERB ijassa-713 83 10 utility utility NOUN ijassa-713 83 11 theory theory NOUN ijassa-713 83 12 . . PUNCT ijassa-713 84 1 thus thus ADV ijassa-713 84 2 , , PUNCT ijassa-713 84 3 a a DET ijassa-713 84 4 special special ADJ ijassa-713 84 5 case case NOUN ijassa-713 84 6 of of ADP ijassa-713 84 7 hyperbolic hyperbolic ADJ ijassa-713 84 8 absolute absolute ADJ ijassa-713 84 9 risk risk NOUN ijassa-713 84 10 aversion aversion NOUN ijassa-713 84 11 ( ( PUNCT ijassa-713 84 12 hara hara PROPN ijassa-713 84 13 ) ) PUNCT ijassa-713 84 14 is be AUX ijassa-713 84 15 considered consider VERB ijassa-713 84 16 as as SCONJ ijassa-713 84 17 the the DET ijassa-713 84 18 model model NOUN ijassa-713 84 19 ’s ’s PART ijassa-713 84 20 utility utility NOUN ijassa-713 84 21 function function NOUN ijassa-713 84 22 which which PRON ijassa-713 84 23 helps help VERB ijassa-713 84 24 in in ADP ijassa-713 84 25 focusing focus VERB ijassa-713 84 26 more more ADV ijassa-713 84 27 on on ADP ijassa-713 84 28 ratios ratio NOUN ijassa-713 84 29 and and CCONJ ijassa-713 84 30 its its PRON ijassa-713 84 31 assumption assumption NOUN ijassa-713 84 32 also also ADV ijassa-713 84 33 lowers lower VERB ijassa-713 84 34 the the DET ijassa-713 84 35 dimension dimension NOUN ijassa-713 84 36 of of ADP ijassa-713 84 37 dynamic dynamic ADJ ijassa-713 84 38 system system NOUN ijassa-713 84 39 for for ADP ijassa-713 84 40 the the DET ijassa-713 84 41 model model NOUN ijassa-713 84 42 to to PART ijassa-713 84 43 be be AUX ijassa-713 84 44 effortlessly effortlessly ADV ijassa-713 84 45 solved solve VERB ijassa-713 84 46 analytically analytically ADV ijassa-713 84 47 unlike unlike ADP ijassa-713 84 48 some some DET ijassa-713 84 49 other other ADJ ijassa-713 84 50 utility utility NOUN ijassa-713 84 51 functions function NOUN ijassa-713 84 52 . . PUNCT ijassa-713 85 1 that that PRON ijassa-713 85 2 is be AUX ijassa-713 85 3 π‘ˆ(𝐴 π‘ˆ(𝐴 PROPN ijassa-713 85 4 ) ) PUNCT ijassa-713 86 1 = = PUNCT ijassa-713 86 2 ( ( PUNCT ijassa-713 86 3 1 1 NUM ijassa-713 86 4 πœ† πœ† X ijassa-713 86 5 π΄πœ† π΄πœ† PROPN ijassa-713 86 6 , , PUNCT ijassa-713 86 7 0 0 PUNCT ijassa-713 86 8 < < X ijassa-713 86 9 πœ† πœ† X ijassa-713 86 10 < < X ijassa-713 86 11 1 1 NUM ijassa-713 86 12 lna lna PROPN ijassa-713 86 13 , , PUNCT ijassa-713 86 14 πœ† πœ† PROPN ijassa-713 86 15 = = SYM ijassa-713 86 16 0 0 NUM ijassa-713 86 17 ( ( PUNCT ijassa-713 86 18 3.2 3.2 NUM ijassa-713 86 19 ) ) PUNCT ijassa-713 86 20 where where SCONJ ijassa-713 86 21 1 1 NUM ijassa-713 86 22 βˆ’ βˆ’ NOUN ijassa-713 86 23 πœ† πœ† NOUN ijassa-713 86 24 > > X ijassa-713 86 25 0 0 NUM ijassa-713 86 26 is be AUX ijassa-713 86 27 the the DET ijassa-713 86 28 investor investor NOUN ijassa-713 86 29 ’s ’s PART ijassa-713 86 30 relative relative ADJ ijassa-713 86 31 risk risk NOUN ijassa-713 86 32 aversion aversion NOUN ijassa-713 86 33 . . PUNCT ijassa-713 87 1 the the PRON ijassa-713 87 2 larger large ADJ ijassa-713 87 3 the the DET ijassa-713 87 4 πœ† πœ† NOUN ijassa-713 87 5 , , PUNCT ijassa-713 87 6 the the DET ijassa-713 87 7 more more ADV ijassa-713 87 8 reluctant reluctant ADJ ijassa-713 87 9 to to PART ijassa-713 87 10 own own VERB ijassa-713 87 11 a a DET ijassa-713 87 12 risky risky ADJ ijassa-713 87 13 asset asset NOUN ijassa-713 87 14 , , PUNCT ijassa-713 88 1 [ [ X ijassa-713 88 2 12 12 NUM ijassa-713 88 3 ] ] PUNCT ijassa-713 88 4 . . PUNCT ijassa-713 89 1 the the DET ijassa-713 89 2 efficiency efficiency NOUN ijassa-713 89 3 or or CCONJ ijassa-713 89 4 performance performance NOUN ijassa-713 89 5 of of ADP ijassa-713 89 6 the the DET ijassa-713 89 7 capital capital NOUN ijassa-713 89 8 asset asset PROPN ijassa-713 89 9 , , PUNCT ijassa-713 89 10 πœ“ πœ“ PROPN ijassa-713 89 11 , , PUNCT ijassa-713 89 12 is be AUX ijassa-713 89 13 expressed express VERB ijassa-713 89 14 as as ADP ijassa-713 89 15 the the DET ijassa-713 89 16 ratio ratio NOUN ijassa-713 89 17 of of ADP ijassa-713 89 18 capital capital NOUN ijassa-713 89 19 asset asset NOUN ijassa-713 89 20 , , PUNCT ijassa-713 89 21 𝐴(𝑑 𝐴(𝑑 NOUN ijassa-713 89 22 ) ) PUNCT ijassa-713 89 23 , , PUNCT ijassa-713 89 24 and and CCONJ ijassa-713 89 25 net net ADJ ijassa-713 89 26 worth worth NOUN ijassa-713 89 27 , , PUNCT ijassa-713 89 28 𝑋(𝑑 𝑋(𝑑 PROPN ijassa-713 89 29 ) ) PUNCT ijassa-713 89 30 , , PUNCT ijassa-713 89 31 such such ADJ ijassa-713 89 32 that that SCONJ ijassa-713 89 33 𝑋(𝑑 𝑋(𝑑 NOUN ijassa-713 89 34 ) ) PUNCT ijassa-713 89 35 β‰  β‰  PROPN ijassa-713 89 36 0 0 NUM ijassa-713 89 37 , , PUNCT ijassa-713 89 38 [ [ X ijassa-713 89 39 15 15 NUM ijassa-713 89 40 ] ] PUNCT ijassa-713 89 41 . . PUNCT ijassa-713 90 1 that that PRON ijassa-713 90 2 is be AUX ijassa-713 90 3 , , PUNCT ijassa-713 90 4 πœ“ πœ“ X ijassa-713 90 5 = = SYM ijassa-713 90 6 𝐴(𝑑 𝐴(𝑑 PROPN ijassa-713 90 7 ) ) PUNCT ijassa-713 90 8 𝑋(𝑑 𝑋(𝑑 PROPN ijassa-713 90 9 ) ) PUNCT ijassa-713 90 10 ( ( PUNCT ijassa-713 90 11 3.3 3.3 NUM ijassa-713 90 12 ) ) PUNCT ijassa-713 90 13 𝐴(𝑑 𝐴(𝑑 NOUN ijassa-713 90 14 ) ) PUNCT ijassa-713 91 1 = = SYM ijassa-713 91 2 πœ“π‘‹(𝑑 πœ“π‘‹(𝑑 PROPN ijassa-713 91 3 ) ) PUNCT ijassa-713 91 4 from from ADP ijassa-713 91 5 the the DET ijassa-713 91 6 proceeding proceeding NOUN ijassa-713 91 7 , , PUNCT ijassa-713 91 8 the the DET ijassa-713 91 9 model model NOUN ijassa-713 91 10 of of ADP ijassa-713 91 11 risky risky ADJ ijassa-713 91 12 capital capital NOUN ijassa-713 91 13 asset asset NOUN ijassa-713 91 14 is be AUX ijassa-713 91 15 an an DET ijassa-713 91 16 optimal optimal ADJ ijassa-713 91 17 control control NOUN ijassa-713 91 18 of of ADP ijassa-713 91 19 the the DET ijassa-713 91 20 form form NOUN ijassa-713 91 21 . . PUNCT ijassa-713 92 1 𝐽(πœ“ 𝐽(πœ“ X ijassa-713 92 2 ) ) PUNCT ijassa-713 92 3 = = SYM ijassa-713 92 4 maxπœ“πΈπΆ maxπœ“πΈπΆ PROPN ijassa-713 92 5 [ [ PUNCT ijassa-713 92 6 ∫ ∫ PROPN ijassa-713 92 7 𝑑𝑛 𝑑𝑛 ADJ ijassa-713 92 8 𝑑0 𝑑0 PROPN ijassa-713 92 9 1 1 NUM ijassa-713 92 10 πœ† πœ† NOUN ijassa-713 92 11 π‘’βˆ’πœ‚π‘‘(πœ“π‘‹(𝑑))πœ†π‘‘π‘‘ π‘’βˆ’πœ‚π‘‘(πœ“π‘‹(𝑑))πœ†π‘‘π‘‘ NOUN ijassa-713 92 12 ] ] X ijassa-713 92 13 ( ( PUNCT ijassa-713 92 14 3.4 3.4 NUM ijassa-713 92 15 ) ) PUNCT ijassa-713 92 16 subject subject NOUN ijassa-713 92 17 to to ADP ijassa-713 92 18 𝑑𝑋(𝑑 𝑑𝑋(𝑑 NUM ijassa-713 92 19 ) ) PUNCT ijassa-713 92 20 = = PUNCT ijassa-713 93 1 [ [ X ijassa-713 93 2 ( ( PUNCT ijassa-713 93 3 πœ… πœ… PRON ijassa-713 93 4 + + X ijassa-713 93 5 𝛽)πœ“ 𝛽)πœ“ ADJ ijassa-713 93 6 βˆ’ βˆ’ PROPN ijassa-713 93 7 ( ( PUNCT ijassa-713 93 8 πœ”(πœ“ πœ”(πœ“ PROPN ijassa-713 93 9 βˆ’ βˆ’ PROPN ijassa-713 93 10 1 1 NUM ijassa-713 93 11 ) ) PUNCT ijassa-713 93 12 + + CCONJ ijassa-713 93 13 πœ‡ πœ‡ ADP ijassa-713 93 14 + + NOUN ijassa-713 93 15 β„Ž β„Ž PART ijassa-713 93 16 βˆ’ βˆ’ NOUN ijassa-713 93 17 𝑗 𝑗 INTJ ijassa-713 93 18 βˆ’ βˆ’ NOUN ijassa-713 93 19 𝑔)]𝑋(𝑑)𝑑𝑑 𝑔)]𝑋(𝑑)𝑑𝑑 ADJ ijassa-713 93 20 + + PROPN ijassa-713 93 21 [ [ X ijassa-713 93 22 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 93 23 + + CCONJ ijassa-713 93 24 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 93 25 βˆ’ βˆ’ NOUN ijassa-713 93 26 πœŽπ‘Ÿ(πœ“ πœŽπ‘Ÿ(πœ“ PUNCT ijassa-713 93 27 βˆ’ βˆ’ PROPN ijassa-713 94 1 1)]𝑋(𝑑)𝑑𝐢(𝑑 1)]𝑋(𝑑)𝑑𝐢(𝑑 NUM ijassa-713 94 2 ) ) PUNCT ijassa-713 95 1 [ [ X ijassa-713 95 2 6 6 NUM ijassa-713 95 3 ] ] PUNCT ijassa-713 95 4 ( ( PUNCT ijassa-713 95 5 3.5 3.5 NUM ijassa-713 95 6 ) ) PUNCT ijassa-713 95 7 4 4 NUM ijassa-713 95 8 . . PUNCT ijassa-713 95 9 application application NOUN ijassa-713 95 10 of of ADP ijassa-713 95 11 the the DET ijassa-713 95 12 capital capital NOUN ijassa-713 95 13 asset asset NOUN ijassa-713 95 14 model model NOUN ijassa-713 95 15 here here ADV ijassa-713 95 16 , , PUNCT ijassa-713 95 17 the the DET ijassa-713 95 18 model model NOUN ijassa-713 95 19 is be AUX ijassa-713 95 20 analysed analyse VERB ijassa-713 95 21 using use VERB ijassa-713 95 22 real real ADJ ijassa-713 95 23 life life NOUN ijassa-713 95 24 data datum NOUN ijassa-713 95 25 in in ADP ijassa-713 95 26 order order NOUN ijassa-713 95 27 to to PART ijassa-713 95 28 provide provide VERB ijassa-713 95 29 some some DET ijassa-713 95 30 optimal optimal ADJ ijassa-713 95 31 solutions solution NOUN ijassa-713 95 32 satisfying satisfy VERB ijassa-713 95 33 the the DET ijassa-713 95 34 optimality optimality NOUN ijassa-713 95 35 criteria criterion NOUN ijassa-713 95 36 . . PUNCT ijassa-713 96 1 utilizing utilize VERB ijassa-713 96 2 the the DET ijassa-713 96 3 model model NOUN ijassa-713 96 4 in in ADP ijassa-713 96 5 international international ADJ ijassa-713 96 6 finance finance NOUN ijassa-713 96 7 , , PUNCT ijassa-713 96 8 the the DET ijassa-713 96 9 revenue revenue NOUN ijassa-713 96 10 is be AUX ijassa-713 96 11 taken take VERB ijassa-713 96 12 to to PART ijassa-713 96 13 be be AUX ijassa-713 96 14 the the DET ijassa-713 96 15 gross gross ADJ ijassa-713 96 16 domestic domestic ADJ ijassa-713 96 17 product product NOUN ijassa-713 96 18 of of ADP ijassa-713 96 19 a a DET ijassa-713 96 20 nation nation NOUN ijassa-713 96 21 ( ( PUNCT ijassa-713 96 22 gdp gdp NOUN ijassa-713 96 23 ) ) PUNCT ijassa-713 96 24 or or CCONJ ijassa-713 96 25 value value NOUN ijassa-713 96 26 added add VERB ijassa-713 96 27 , , PUNCT ijassa-713 96 28 the the DET ijassa-713 96 29 risky risky ADJ ijassa-713 96 30 capital capital NOUN ijassa-713 96 31 asset asset NOUN ijassa-713 96 32 as as ADP ijassa-713 96 33 the the DET ijassa-713 96 34 capital capital NOUN ijassa-713 96 35 investment investment NOUN ijassa-713 96 36 or or CCONJ ijassa-713 96 37 the the DET ijassa-713 96 38 gross gross ADJ ijassa-713 96 39 fixed fix VERB ijassa-713 96 40 capital capital NOUN ijassa-713 96 41 formation formation NOUN ijassa-713 96 42 , , PUNCT ijassa-713 96 43 consumption consumption NOUN ijassa-713 96 44 as as ADP ijassa-713 96 45 household household NOUN ijassa-713 96 46 and and CCONJ ijassa-713 96 47 government government NOUN ijassa-713 96 48 consumption consumption NOUN ijassa-713 96 49 , , PUNCT ijassa-713 96 50 depreciation depreciation NOUN ijassa-713 96 51 is be AUX ijassa-713 96 52 taken take VERB ijassa-713 96 53 as as ADP ijassa-713 96 54 the the DET ijassa-713 96 55 consumption consumption NOUN ijassa-713 96 56 of of ADP ijassa-713 96 57 fixed fix VERB ijassa-713 96 58 capital capital NOUN ijassa-713 96 59 . . PUNCT ijassa-713 97 1 the the DET ijassa-713 97 2 debt debt NOUN ijassa-713 97 3 is be AUX ijassa-713 97 4 also also ADV ijassa-713 97 5 taken take VERB ijassa-713 97 6 as as ADP ijassa-713 97 7 a a DET ijassa-713 97 8 study study NOUN ijassa-713 97 9 case case NOUN ijassa-713 97 10 of of ADP ijassa-713 97 11 liability liability NOUN ijassa-713 97 12 to to PART ijassa-713 97 13 be be AUX ijassa-713 97 14 considered consider VERB ijassa-713 97 15 . . PUNCT ijassa-713 98 1 table table NOUN ijassa-713 98 2 4.1 4.1 NUM ijassa-713 98 3 : : PUNCT ijassa-713 98 4 definition definition NOUN ijassa-713 98 5 of of ADP ijassa-713 98 6 parameters parameter NOUN ijassa-713 98 7 according accord VERB ijassa-713 98 8 to to ADP ijassa-713 98 9 the the DET ijassa-713 98 10 model model NOUN ijassa-713 98 11 application application NOUN ijassa-713 98 12 parameter parameter NOUN ijassa-713 98 13 description description NOUN ijassa-713 98 14 𝐽 𝐽 PROPN ijassa-713 98 15 expected expect VERB ijassa-713 98 16 present present ADJ ijassa-713 98 17 value value NOUN ijassa-713 98 18 of of ADP ijassa-713 98 19 utility utility NOUN ijassa-713 98 20 of of ADP ijassa-713 98 21 gfcf gfcf NOUN ijassa-713 98 22 t. t. PROPN ijassa-713 98 23 latunde latunde VERB ijassa-713 98 24 57 57 NUM ijassa-713 98 25 copyright copyright NOUN ijassa-713 98 26 Β© Β© PROPN ijassa-713 98 27 2019 2019 NUM ijassa-713 98 28 assa assa NOUN ijassa-713 98 29 . . PUNCT ijassa-713 99 1 adv adv PROPN ijassa-713 99 2 . . PUNCT ijassa-713 100 1 in in ADP ijassa-713 100 2 systems system NOUN ijassa-713 100 3 science science NOUN ijassa-713 100 4 and and CCONJ ijassa-713 100 5 appl appl NOUN ijassa-713 100 6 . . PUNCT ijassa-713 101 1 ( ( PUNCT ijassa-713 101 2 2019 2019 NUM ijassa-713 101 3 ) ) PUNCT ijassa-713 101 4 πœ‚ πœ‚ PRON ijassa-713 101 5 subjective subjective ADJ ijassa-713 101 6 discount discount NOUN ijassa-713 101 7 rate rate NOUN ijassa-713 101 8 , , PUNCT ijassa-713 101 9 e.g. e.g. ADV ijassa-713 101 10 , , PUNCT ijassa-713 101 11 𝐴 𝐴 PROPN ijassa-713 101 12 πœ‚+1 πœ‚+1 X ijassa-713 101 13 = = SYM ijassa-713 101 14 presentvalue presentvalue PROPN ijassa-713 101 15 πœ† πœ† DET ijassa-713 101 16 degree degree NOUN ijassa-713 101 17 of of ADP ijassa-713 101 18 relative relative ADJ ijassa-713 101 19 risk risk NOUN ijassa-713 101 20 , , PUNCT ijassa-713 101 21 where where SCONJ ijassa-713 101 22 ( ( PUNCT ijassa-713 101 23 1 1 NUM ijassa-713 101 24 βˆ’ βˆ’ NOUN ijassa-713 101 25 πœ† πœ† NOUN ijassa-713 101 26 ) ) PUNCT ijassa-713 101 27 is be AUX ijassa-713 101 28 the the DET ijassa-713 101 29 risk risk NOUN ijassa-713 101 30 aversion aversion NOUN ijassa-713 101 31 πœ“ πœ“ PROPN ijassa-713 101 32 gfcf gfcf PROPN ijassa-713 101 33 ratio ratio PROPN ijassa-713 101 34 ( ( PUNCT ijassa-713 101 35 control control NOUN ijassa-713 101 36 ) ) PUNCT ijassa-713 101 37 πœ“ πœ“ PROPN ijassa-713 101 38 ∈ ∈ PROPN ijassa-713 101 39 β„œ β„œ PROPN ijassa-713 101 40 𝜏(𝑑 𝜏(𝑑 NOUN ijassa-713 101 41 ) ) PUNCT ijassa-713 101 42 debt debt NOUN ijassa-713 101 43 ratio ratio NOUN ijassa-713 101 44 ( ( PUNCT ijassa-713 101 45 control control NOUN ijassa-713 101 46 ) ) PUNCT ijassa-713 101 47 at at ADP ijassa-713 101 48 time time NOUN ijassa-713 101 49 𝑑 𝑑 PROPN ijassa-713 101 50 , , PUNCT ijassa-713 101 51 𝜏 𝜏 NOUN ijassa-713 101 52 = = SYM ijassa-713 101 53 πœ“ πœ“ NOUN ijassa-713 101 54 βˆ’ βˆ’ PROPN ijassa-713 101 55 1 1 NUM ijassa-713 101 56 𝑋(𝑑 𝑋(𝑑 NOUN ijassa-713 101 57 ) ) PUNCT ijassa-713 101 58 net net ADJ ijassa-713 101 59 worth worth NOUN ijassa-713 101 60 at at ADP ijassa-713 101 61 time time NOUN ijassa-713 101 62 𝑑 𝑑 PROPN ijassa-713 101 63 ( ( PUNCT ijassa-713 101 64 gfcf gfcf PROPN ijassa-713 101 65 minus minus CCONJ ijassa-713 101 66 debt debt NOUN ijassa-713 101 67 ) ) PUNCT ijassa-713 101 68 πœ…(𝑑 πœ…(𝑑 ADJ ijassa-713 101 69 ) ) PUNCT ijassa-713 101 70 capital capital NOUN ijassa-713 101 71 gain gain NOUN ijassa-713 101 72 on on ADP ijassa-713 101 73 gfcf gfcf NOUN ijassa-713 101 74 with with ADP ijassa-713 101 75 net net ADJ ijassa-713 101 76 worth worth NOUN ijassa-713 101 77 at at ADP ijassa-713 101 78 time time NOUN ijassa-713 101 79 𝑑 𝑑 X ijassa-713 101 80 𝛽(𝑑 𝛽(𝑑 PROPN ijassa-713 101 81 ) ) PUNCT ijassa-713 101 82 mean mean VERB ijassa-713 101 83 rate rate NOUN ijassa-713 101 84 of of ADP ijassa-713 101 85 return return NOUN ijassa-713 101 86 on on ADP ijassa-713 101 87 gfcf gfcf NOUN ijassa-713 101 88 with with ADP ijassa-713 101 89 net net ADJ ijassa-713 101 90 worth worth NOUN ijassa-713 101 91 πœ”(𝑑 πœ”(𝑑 PROPN ijassa-713 101 92 ) ) PUNCT ijassa-713 101 93 mean mean ADJ ijassa-713 101 94 rate rate NOUN ijassa-713 101 95 of of ADP ijassa-713 101 96 debt debt NOUN ijassa-713 101 97 with with ADP ijassa-713 101 98 net net ADJ ijassa-713 101 99 worth worth ADJ ijassa-713 101 100 πœŽπ‘(𝑑 πœŽπ‘(𝑑 NUM ijassa-713 101 101 ) ) PUNCT ijassa-713 101 102 diffusion diffusion NOUN ijassa-713 101 103 volatility volatility NOUN ijassa-713 101 104 on on ADP ijassa-713 101 105 asset asset NOUN ijassa-713 101 106 price price NOUN ijassa-713 101 107 ( ( PUNCT ijassa-713 101 108 with with ADP ijassa-713 101 109 variance variance NOUN ijassa-713 101 110 πœŽπ‘ πœŽπ‘ ADP ijassa-713 101 111 2 2 NUM ijassa-713 101 112 per per ADP ijassa-713 101 113 unit unit NOUN ijassa-713 101 114 time time NOUN ijassa-713 101 115 ) ) PUNCT ijassa-713 101 116 πœŽπ‘(𝑑 πœŽπ‘(𝑑 NOUN ijassa-713 101 117 ) ) PUNCT ijassa-713 101 118 diffusion diffusion NOUN ijassa-713 101 119 volatility volatility NOUN ijassa-713 101 120 of of ADP ijassa-713 101 121 gfcf gfcf NOUN ijassa-713 101 122 ( ( PUNCT ijassa-713 101 123 with with ADP ijassa-713 101 124 variance variance NOUN ijassa-713 101 125 πœŽπ‘ πœŽπ‘ PROPN ijassa-713 101 126 2 2 NUM ijassa-713 101 127 per per ADP ijassa-713 101 128 unit unit NOUN ijassa-713 101 129 time time NOUN ijassa-713 101 130 ) ) PUNCT ijassa-713 101 131 πœŽπ‘Ÿ(𝑑 πœŽπ‘Ÿ(𝑑 NUM ijassa-713 101 132 ) ) PUNCT ijassa-713 101 133 diffusion diffusion NOUN ijassa-713 101 134 volatility volatility NOUN ijassa-713 101 135 of of ADP ijassa-713 101 136 debt debt NOUN ijassa-713 101 137 ( ( PUNCT ijassa-713 101 138 with with ADP ijassa-713 101 139 variance variance NOUN ijassa-713 101 140 πœŽπ‘Ÿ πœŽπ‘Ÿ ADP ijassa-713 101 141 2 2 NUM ijassa-713 101 142 per per ADP ijassa-713 101 143 unit unit NOUN ijassa-713 101 144 time time NOUN ijassa-713 101 145 ) ) PUNCT ijassa-713 101 146 𝜎(𝑑 𝜎(𝑑 NUM ijassa-713 101 147 ) ) PUNCT ijassa-713 101 148 diffusion diffusion NOUN ijassa-713 101 149 volatility volatility NOUN ijassa-713 101 150 of of ADP ijassa-713 101 151 the the DET ijassa-713 101 152 whole whole ADJ ijassa-713 101 153 process process NOUN ijassa-713 101 154 ( ( PUNCT ijassa-713 101 155 πœŽπ‘ πœŽπ‘ NOUN ijassa-713 101 156 + + NUM ijassa-713 101 157 πœŽπ‘ πœŽπ‘ PROPN ijassa-713 101 158 βˆ’ βˆ’ PROPN ijassa-713 101 159 πœŽπœ” πœŽπœ” PROPN ijassa-713 101 160 ) ) PUNCT ijassa-713 101 161 , , PUNCT ijassa-713 101 162 [ [ X ijassa-713 101 163 15 15 NUM ijassa-713 101 164 ] ] X ijassa-713 101 165 πœ‡(𝑑 πœ‡(𝑑 NOUN ijassa-713 101 166 ) ) PUNCT ijassa-713 101 167 consumption consumption NOUN ijassa-713 101 168 level level NOUN ijassa-713 101 169 with with ADP ijassa-713 101 170 net net ADJ ijassa-713 101 171 worth worth NOUN ijassa-713 101 172 at at ADP ijassa-713 101 173 time time NOUN ijassa-713 101 174 𝑑 𝑑 X ijassa-713 101 175 𝑠(𝑑 𝑠(𝑑 PROPN ijassa-713 101 176 ) ) PUNCT ijassa-713 101 177 net net ADJ ijassa-713 101 178 foreign foreign ADJ ijassa-713 101 179 supplies supply NOUN ijassa-713 101 180 net net ADJ ijassa-713 101 181 worth worth ADJ ijassa-713 101 182 ratio ratio NOUN ijassa-713 101 183 at at ADP ijassa-713 101 184 time time NOUN ijassa-713 101 185 𝑑 𝑑 PROPN ijassa-713 101 186 𝑗(𝑑 𝑗(𝑑 PROPN ijassa-713 101 187 ) ) PUNCT ijassa-713 101 188 tax tax NOUN ijassa-713 101 189 - - PUNCT ijassa-713 101 190 net net NOUN ijassa-713 101 191 worth worth ADJ ijassa-713 101 192 ratio ratio NOUN ijassa-713 101 193 at at ADP ijassa-713 101 194 time time NOUN ijassa-713 101 195 𝑑 𝑑 PROPN ijassa-713 101 196 𝑔(𝑑 𝑔(𝑑 NOUN ijassa-713 101 197 ) ) PUNCT ijassa-713 101 198 depreciation depreciation NOUN ijassa-713 101 199 - - PUNCT ijassa-713 101 200 net net NOUN ijassa-713 101 201 worth worth ADJ ijassa-713 101 202 ratio ratio NOUN ijassa-713 101 203 at at ADP ijassa-713 101 204 time time NOUN ijassa-713 101 205 𝑑 𝑑 PROPN ijassa-713 101 206 𝐢(𝑑 𝐢(𝑑 ADJ ijassa-713 101 207 ) ) PUNCT ijassa-713 101 208 liu liu PROPN ijassa-713 101 209 canonical canonical ADJ ijassa-713 101 210 process process NOUN ijassa-713 101 211 at at ADP ijassa-713 101 212 time time NOUN ijassa-713 101 213 𝑑 𝑑 VERB ijassa-713 101 214 in in ADP ijassa-713 101 215 order order NOUN ijassa-713 101 216 to to PART ijassa-713 101 217 examine examine VERB ijassa-713 101 218 the the DET ijassa-713 101 219 debt debt NOUN ijassa-713 101 220 crisis crisis NOUN ijassa-713 101 221 in in ADP ijassa-713 101 222 nigeria nigeria PROPN ijassa-713 101 223 and and CCONJ ijassa-713 101 224 propose propose VERB ijassa-713 101 225 a a DET ijassa-713 101 226 warning warning NOUN ijassa-713 101 227 signal signal NOUN ijassa-713 101 228 , , PUNCT ijassa-713 101 229 the the DET ijassa-713 101 230 data datum NOUN ijassa-713 101 231 that that PRON ijassa-713 101 232 are be AUX ijassa-713 101 233 available available ADJ ijassa-713 101 234 after after SCONJ ijassa-713 101 235 the the DET ijassa-713 101 236 paris paris PROPN ijassa-713 101 237 debt debt NOUN ijassa-713 101 238 forgiveness forgiveness NOUN ijassa-713 101 239 in in ADP ijassa-713 101 240 2006 2006 NUM ijassa-713 101 241 are be AUX ijassa-713 101 242 used use VERB ijassa-713 101 243 . . PUNCT ijassa-713 102 1 thus thus ADV ijassa-713 102 2 , , PUNCT ijassa-713 102 3 tables table VERB ijassa-713 102 4 4.2 4.2 NUM ijassa-713 102 5 and and CCONJ ijassa-713 102 6 4.3 4.3 NUM ijassa-713 102 7 below below ADV ijassa-713 102 8 represent represent VERB ijassa-713 102 9 the the DET ijassa-713 102 10 base base NOUN ijassa-713 102 11 parameter parameter NOUN ijassa-713 102 12 set set VERB ijassa-713 102 13 for for ADP ijassa-713 102 14 the the DET ijassa-713 102 15 case case NOUN ijassa-713 102 16 study study NOUN ijassa-713 102 17 . . PUNCT ijassa-713 103 1 table table NOUN ijassa-713 103 2 4.2 4.2 NUM ijassa-713 103 3 : : PUNCT ijassa-713 103 4 nigeria nigeria PROPN ijassa-713 103 5 net net PROPN ijassa-713 103 6 worth worth ADJ ijassa-713 103 7 profile profile PROPN ijassa-713 103 8 year year NOUN ijassa-713 103 9 gdp gdp NOUN ijassa-713 103 10 debt debt PROPN ijassa-713 103 11 gfcf gfcf PROPN ijassa-713 103 12 net net PROPN ijassa-713 103 13 worth worth ADJ ijassa-713 103 14 consumption consumption NOUN ijassa-713 103 15 indirect indirect ADJ ijassa-713 103 16 tax tax NOUN ijassa-713 103 17 depreciation depreciation NOUN ijassa-713 103 18 supplies supply NOUN ijassa-713 103 19 2007 2007 NUM ijassa-713 103 20 166.451 166.451 NUM ijassa-713 103 21 22.330 22.330 NUM ijassa-713 103 22 15.396 15.396 NUM ijassa-713 103 23 -6.934 -6.934 NOUN ijassa-713 103 24 149 149 NUM ijassa-713 103 25 . . PUNCT ijassa-713 104 1 152 152 NUM ijassa-713 104 2 2.553 2.553 NUM ijassa-713 104 3 3.738 3.738 NUM ijassa-713 104 4 5.089 5.089 NUM ijassa-713 104 5 2008 2008 NUM ijassa-713 104 6 208.065 208.065 NUM ijassa-713 104 7 21.399 21.399 NUM ijassa-713 104 8 17.318 17.318 NUM ijassa-713 104 9 -4.081 -4.081 NUM ijassa-713 104 10 161.035 161.035 NUM ijassa-713 104 11 3.436 3.436 NUM ijassa-713 104 12 3.853 3.853 NUM ijassa-713 104 13 30.988 30.988 NUM ijassa-713 104 14 2009 2009 NUM ijassa-713 104 15 169.481 169.481 NUM ijassa-713 104 16 25.817 25.817 NUM ijassa-713 104 17 20.487 20.487 NUM ijassa-713 104 18 -5.330 -5.330 PROPN ijassa-713 104 19 147.601 147.601 NUM ijassa-713 104 20 3.180 3.180 NUM ijassa-713 104 21 2.952 2.952 NUM ijassa-713 104 22 0.445 0.445 NUM ijassa-713 104 23 2010 2010 NUM ijassa-713 104 24 369.062 369.062 NUM ijassa-713 104 25 40.100 40.100 NUM ijassa-713 104 26 61.099 61.099 NUM ijassa-713 104 27 21.860 21.860 NUM ijassa-713 104 28 293.507 293.507 NUM ijassa-713 104 29 5.623 5.623 NUM ijassa-713 104 30 16.079 16.079 NUM ijassa-713 104 31 28.662 28.662 NUM ijassa-713 104 32 2011 2011 NUM ijassa-713 104 33 411.744 411.744 NUM ijassa-713 104 34 47.898 47.898 NUM ijassa-713 104 35 63.960 63.960 NUM ijassa-713 104 36 16.062 16.062 NUM ijassa-713 104 37 323.540 323.540 NUM ijassa-713 104 38 4.516 4.516 NUM ijassa-713 104 39 18.815 18.815 NUM ijassa-713 104 40 38.719 38.719 NUM ijassa-713 104 41 2012 2012 NUM ijassa-713 104 42 460.953 460.953 NUM ijassa-713 104 43 48.496 48.496 NUM ijassa-713 104 44 65.283 65.283 NUM ijassa-713 104 45 16.787 16.787 NUM ijassa-713 104 46 348.597 348.597 NUM ijassa-713 104 47 5.686 5.686 NUM ijassa-713 104 48 24.260 24.260 NUM ijassa-713 104 49 86.210 86.210 NUM ijassa-713 104 50 2013 2013 NUM ijassa-713 104 51 514.966 514.966 NUM ijassa-713 104 52 64.510 64.510 NUM ijassa-713 104 53 72.964 72.964 NUM ijassa-713 104 54 8.454 8.454 NUM ijassa-713 104 55 453.699 453.699 NUM ijassa-713 104 56 7.929 7.929 NUM ijassa-713 104 57 23.857 23.857 NUM ijassa-713 104 58 26.280 26.280 NUM ijassa-713 104 59 2014 2014 NUM ijassa-713 104 60 568.499 568.499 NUM ijassa-713 104 61 67.726 67.726 NUM ijassa-713 104 62 85.737 85.737 NUM ijassa-713 104 63 18.011 18.011 NUM ijassa-713 104 64 464.696 464.696 NUM ijassa-713 104 65 6.857 6.857 NUM ijassa-713 104 66 25.272 25.272 NUM ijassa-713 104 67 32.499 32.499 NUM ijassa-713 104 68 2015 2015 NUM ijassa-713 104 69 481.066 481.066 NUM ijassa-713 104 70 65.429 65.429 NUM ijassa-713 104 71 71.329 71.329 NUM ijassa-713 104 72 5.900 5.900 NUM ijassa-713 104 73 417.560 417.560 NUM ijassa-713 104 74 5.362 5.362 NUM ijassa-713 104 75 23.097 23.097 NUM ijassa-713 104 76 0.000 0.000 NUM ijassa-713 104 77 2016 2016 NUM ijassa-713 104 78 405.083 405.083 NUM ijassa-713 104 79 57.392 57.392 NUM ijassa-713 104 80 73.261 73.261 NUM ijassa-713 104 81 15.869 15.869 NUM ijassa-713 104 82 206.414 206.414 NUM ijassa-713 104 83 3.188 3.188 NUM ijassa-713 104 84 10.332 10.332 NUM ijassa-713 104 85 -3.341 -3.341 PUNCT ijassa-713 104 86 source source NOUN ijassa-713 104 87 : : PUNCT ijassa-713 104 88 columns column NOUN ijassa-713 104 89 1 1 NUM ijassa-713 104 90 and and CCONJ ijassa-713 104 91 3 3 NUM ijassa-713 104 92 . . X ijassa-713 105 1 the the DET ijassa-713 105 2 world world PROPN ijassa-713 105 3 bank bank PROPN ijassa-713 105 4 ( ( PUNCT ijassa-713 105 5 http://data.worldbank.org/indicator http://data.worldbank.org/indicator NOUN ijassa-713 105 6 ) ) PUNCT ijassa-713 105 7 column column NOUN ijassa-713 105 8 2 2 NUM ijassa-713 105 9 . . PUNCT ijassa-713 105 10 debt debt NOUN ijassa-713 105 11 management management NOUN ijassa-713 105 12 office office NOUN ijassa-713 105 13 of of ADP ijassa-713 105 14 nigeria nigeria PROPN ijassa-713 105 15 ( ( PUNCT ijassa-713 105 16 https://www.dmo.gov.ng/ https://www.dmo.gov.ng/ PROPN ijassa-713 105 17 ) ) PUNCT ijassa-713 105 18 . . PUNCT ijassa-713 106 1 columns column NOUN ijassa-713 106 2 5 5 NUM ijassa-713 106 3 , , PUNCT ijassa-713 106 4 6 6 NUM ijassa-713 106 5 , , PUNCT ijassa-713 106 6 7 7 NUM ijassa-713 106 7 , , PUNCT ijassa-713 106 8 8 8 NUM ijassa-713 106 9 and and CCONJ ijassa-713 106 10 9 9 NUM ijassa-713 106 11 . . X ijassa-713 106 12 national national PROPN ijassa-713 106 13 bureau bureau PROPN ijassa-713 106 14 of of ADP ijassa-713 106 15 statistics statistic NOUN ijassa-713 106 16 ( ( PUNCT ijassa-713 106 17 http://nigerianstat.gov.ng/ http://nigerianstat.gov.ng/ PROPN ijassa-713 106 18 ) ) PUNCT ijassa-713 106 19 table table NOUN ijassa-713 106 20 4.3 4.3 NUM ijassa-713 106 21 is be AUX ijassa-713 106 22 derived derive VERB ijassa-713 106 23 from from ADP ijassa-713 106 24 table table NOUN ijassa-713 106 25 4.2 4.2 NUM ijassa-713 106 26 . . PUNCT ijassa-713 107 1 table table NOUN ijassa-713 107 2 4.3 4.3 NUM ijassa-713 107 3 : : PUNCT ijassa-713 107 4 parameters parameter NOUN ijassa-713 107 5 for for ADP ijassa-713 107 6 the the DET ijassa-713 107 7 nigeria nigeria PROPN ijassa-713 107 8 net net PROPN ijassa-713 107 9 worth worth ADJ ijassa-713 107 10 profile profile NOUN ijassa-713 107 11 year year NOUN ijassa-713 107 12 πœ… πœ… PROPN ijassa-713 107 13 𝛽 𝛽 NOUN ijassa-713 107 14 πœ” πœ” PART ijassa-713 107 15 πœŽπ‘ πœŽπ‘ NOUN ijassa-713 107 16 πœŽπ‘ πœŽπ‘ PROPN ijassa-713 107 17 πœŽπ‘Ÿ πœŽπ‘Ÿ ADP ijassa-713 107 18 𝜎 𝜎 PROPN ijassa-713 107 19 πœ‡ πœ‡ ADP ijassa-713 107 20 h h NOUN ijassa-713 107 21 j j PROPN ijassa-713 107 22 g g PROPN ijassa-713 107 23 58 58 NUM ijassa-713 107 24 optimal optimal ADJ ijassa-713 107 25 values value NOUN ijassa-713 107 26 in in ADP ijassa-713 107 27 uncertin uncertin PROPN ijassa-713 107 28 optimal optimal ADJ ijassa-713 107 29 control control NOUN ijassa-713 107 30 model model NOUN ijassa-713 107 31 copyright copyright NOUN ijassa-713 107 32 Β© Β© PROPN ijassa-713 107 33 2019 2019 NUM ijassa-713 107 34 assa assa PROPN ijassa-713 107 35 adv adv PROPN ijassa-713 107 36 . . PUNCT ijassa-713 108 1 in in ADP ijassa-713 108 2 systems system NOUN ijassa-713 108 3 science science NOUN ijassa-713 108 4 and and CCONJ ijassa-713 108 5 appl appl NOUN ijassa-713 108 6 . . PUNCT ijassa-713 109 1 ( ( PUNCT ijassa-713 109 2 2019 2019 NUM ijassa-713 109 3 ) ) PUNCT ijassa-713 109 4 2007 2007 NUM ijassa-713 110 1 -7.25 -7.25 NUM ijassa-713 110 2 -51.72 -51.72 PROPN ijassa-713 110 3 -6.10 -6.10 PRON ijassa-713 110 4 -3.78 -3.78 NUM ijassa-713 110 5 -21.47 -21.47 PROPN ijassa-713 110 6 -2.46 -2.46 NUM ijassa-713 110 7 -22.79 -22.79 PROPN ijassa-713 110 8 -21.51 -21.51 PUNCT ijassa-713 110 9 -0.73 -0.73 ADP ijassa-713 110 10 -0.37 -0.37 NUM ijassa-713 110 11 -0.54 -0.54 NOUN ijassa-713 110 12 2008 2008 NUM ijassa-713 110 13 -12.32 -12.32 SYM ijassa-713 110 14 -87.88 -87.88 SYM ijassa-713 110 15 -10.36 -10.36 PROPN ijassa-713 110 16 -6.42 -6.42 NUM ijassa-713 110 17 -36.48 -36.48 PROPN ijassa-713 110 18 -4.17 -4.17 PROPN ijassa-713 110 19 -38.73 -38.73 PROPN ijassa-713 110 20 -39.46 -39.46 PROPN ijassa-713 110 21 -7.59 -7.59 PUNCT ijassa-713 110 22 -0.77 -0.77 NUM ijassa-713 110 23 -0.94 -0.94 NUM ijassa-713 110 24 2009 2009 NUM ijassa-713 110 25 -9.43 -9.43 NUM ijassa-713 110 26 -67.29 -67.29 SYM ijassa-713 110 27 -7.93 -7.93 NUM ijassa-713 110 28 -4.92 -4.92 PROPN ijassa-713 110 29 -27.93 -27.93 PROPN ijassa-713 110 30 -3.20 -3.20 NUM ijassa-713 110 31 -29.65 -29.65 PROPN ijassa-713 110 32 -27.69 -27.69 PROPN ijassa-713 110 33 0.08 0.08 NUM ijassa-713 110 34 -0.60 -0.60 NUM ijassa-713 110 35 -0.55 -0.55 NUM ijassa-713 110 36 2010 2010 NUM ijassa-713 110 37 2.30 2.30 NUM ijassa-713 110 38 16.41 16.41 NUM ijassa-713 110 39 1.93 1.93 NUM ijassa-713 110 40 1.20 1.20 NUM ijassa-713 110 41 6.81 6.81 NUM ijassa-713 110 42 0.78 0.78 NUM ijassa-713 110 43 7.23 7.23 NUM ijassa-713 110 44 13.43 13.43 NUM ijassa-713 110 45 1.31 1.31 NUM ijassa-713 110 46 0.26 0.26 NUM ijassa-713 110 47 0.74 0.74 NUM ijassa-713 110 48 2011 2011 NUM ijassa-713 110 49 3.13 3.13 NUM ijassa-713 110 50 22.33 22.33 NUM ijassa-713 110 51 2.63 2.63 NUM ijassa-713 110 52 1.63 1.63 NUM ijassa-713 110 53 9.27 9.27 NUM ijassa-713 110 54 1.06 1.06 NUM ijassa-713 110 55 9.84 9.84 NUM ijassa-713 110 56 20.14 20.14 NUM ijassa-713 110 57 2.14 2.14 NUM ijassa-713 110 58 0.28 0.28 NUM ijassa-713 110 59 1.17 1.17 NUM ijassa-713 110 60 2012 2012 NUM ijassa-713 110 61 2.30 2.30 NUM ijassa-713 110 62 21.37 21.37 NUM ijassa-713 110 63 2.52 2.52 NUM ijassa-713 110 64 1.56 1.56 NUM ijassa-713 110 65 8.87 8.87 NUM ijassa-713 110 66 1.02 1.02 NUM ijassa-713 110 67 9.41 9.41 NUM ijassa-713 110 68 20.77 20.77 NUM ijassa-713 110 69 5.14 5.14 NUM ijassa-713 110 70 0.34 0.34 NUM ijassa-713 110 71 1.45 1.45 NUM ijassa-713 110 72 2013 2013 NUM ijassa-713 110 73 5.95 5.95 NUM ijassa-713 110 74 42.42 42.42 NUM ijassa-713 110 75 5.00 5.00 NUM ijassa-713 110 76 3.10 3.10 NUM ijassa-713 110 77 17.61 17.61 NUM ijassa-713 110 78 2.02 2.02 NUM ijassa-713 110 79 18.69 18.69 NUM ijassa-713 110 80 53.67 53.67 NUM ijassa-713 110 81 3.11 3.11 NUM ijassa-713 110 82 0.94 0.94 NUM ijassa-713 110 83 2.82 2.82 NUM ijassa-713 110 84 2014 2014 NUM ijassa-713 110 85 2.79 2.79 NUM ijassa-713 110 86 19.91 19.91 NUM ijassa-713 110 87 1.43 1.43 NUM ijassa-713 110 88 1.46 1.46 NUM ijassa-713 110 89 8.27 8.27 NUM ijassa-713 110 90 0.95 0.95 NUM ijassa-713 110 91 8.78 8.78 NUM ijassa-713 110 92 25.80 25.80 NUM ijassa-713 110 93 1.92 1.92 NUM ijassa-713 110 94 0.37 0.37 NUM ijassa-713 110 95 1.40 1.40 NUM ijassa-713 110 96 2015 2015 NUM ijassa-713 110 97 8.52 8.52 NUM ijassa-713 110 98 60.79 60.79 NUM ijassa-713 110 99 4.37 4.37 NUM ijassa-713 110 100 4.44 4.44 NUM ijassa-713 110 101 25.23 25.23 NUM ijassa-713 110 102 2.89 2.89 NUM ijassa-713 110 103 26.78 26.78 NUM ijassa-713 110 104 70.77 70.77 NUM ijassa-713 110 105 0.00 0.00 NUM ijassa-713 110 106 0.91 0.91 NUM ijassa-713 110 107 3.91 3.91 NUM ijassa-713 110 108 2016 2016 NUM ijassa-713 110 109 3.17 3.17 NUM ijassa-713 110 110 22.60 22.60 NUM ijassa-713 110 111 1.63 1.63 NUM ijassa-713 110 112 1.65 1.65 NUM ijassa-713 110 113 9.38 9.38 NUM ijassa-713 110 114 1.07 1.07 NUM ijassa-713 110 115 9.96 9.96 NUM ijassa-713 110 116 13.01 13.01 NUM ijassa-713 110 117 -0.21 -0.21 NUM ijassa-713 110 118 0.20 0.20 NUM ijassa-713 110 119 0.65 0.65 NUM ijassa-713 110 120 measurements measurement NOUN ijassa-713 111 1 the the DET ijassa-713 111 2 measurements measurement NOUN ijassa-713 111 3 considered consider VERB ijassa-713 111 4 in in ADP ijassa-713 111 5 obtaining obtain VERB ijassa-713 111 6 data datum NOUN ijassa-713 111 7 in in ADP ijassa-713 111 8 tables table NOUN ijassa-713 111 9 4.1 4.1 NUM ijassa-713 111 10 – – PUNCT ijassa-713 111 11 4.3 4.3 NUM ijassa-713 111 12 are be AUX ijassa-713 111 13 described describe VERB ijassa-713 111 14 below below ADV ijassa-713 111 15 . . PUNCT ijassa-713 112 1 all all DET ijassa-713 112 2 the the DET ijassa-713 112 3 values value NOUN ijassa-713 112 4 of of ADP ijassa-713 112 5 parameters parameter NOUN ijassa-713 112 6 are be AUX ijassa-713 112 7 measured measure VERB ijassa-713 112 8 in in ADP ijassa-713 112 9 billion billion NUM ijassa-713 112 10 us us PROPN ijassa-713 112 11 dollars dollar NOUN ijassa-713 112 12 except except SCONJ ijassa-713 112 13 the the DET ijassa-713 112 14 following follow VERB ijassa-713 112 15 parameters parameter NOUN ijassa-713 112 16 : : PUNCT ijassa-713 112 17 𝐢(𝑑 𝐢(𝑑 NUM ijassa-713 112 18 ) ) PUNCT ijassa-713 112 19 measures measure NOUN ijassa-713 112 20 the the DET ijassa-713 112 21 uncertainty uncertainty NOUN ijassa-713 112 22 process process NOUN ijassa-713 112 23 which which PRON ijassa-713 112 24 exists exist VERB ijassa-713 112 25 in in ADP ijassa-713 112 26 the the DET ijassa-713 112 27 interval interval NOUN ijassa-713 112 28 0 0 PUNCT ijassa-713 112 29 < < X ijassa-713 112 30 𝐢(𝑑 𝐢(𝑑 X ijassa-713 112 31 ) ) PUNCT ijassa-713 112 32 < < X ijassa-713 112 33 1 1 NUM ijassa-713 112 34 ; ; PUNCT ijassa-713 112 35 πœ† πœ† X ijassa-713 112 36 is be AUX ijassa-713 112 37 used use VERB ijassa-713 112 38 to to PART ijassa-713 112 39 measure measure VERB ijassa-713 112 40 risk risk NOUN ijassa-713 112 41 which which PRON ijassa-713 112 42 exists exist VERB ijassa-713 112 43 in in ADP ijassa-713 112 44 the the DET ijassa-713 112 45 interval interval NOUN ijassa-713 112 46 0 0 PUNCT ijassa-713 112 47 < < X ijassa-713 112 48 πœ† πœ† X ijassa-713 112 49 < < X ijassa-713 112 50 1 1 NUM ijassa-713 112 51 ; ; PUNCT ijassa-713 112 52 and and CCONJ ijassa-713 112 53 πœ‚ πœ‚ NOUN ijassa-713 112 54 measures measure NOUN ijassa-713 112 55 discount discount NOUN ijassa-713 112 56 rate rate NOUN ijassa-713 112 57 which which PRON ijassa-713 112 58 exists exist VERB ijassa-713 112 59 in in ADP ijassa-713 112 60 the the DET ijassa-713 112 61 interval interval NOUN ijassa-713 112 62 0 0 PUNCT ijassa-713 112 63 < < X ijassa-713 112 64 πœ‚ πœ‚ X ijassa-713 112 65 < < X ijassa-713 112 66 1 1 NUM ijassa-713 112 67 . . PUNCT ijassa-713 113 1 the the DET ijassa-713 113 2 debt debt NOUN ijassa-713 113 3 is be AUX ijassa-713 113 4 calculated calculate VERB ijassa-713 113 5 as as ADP ijassa-713 113 6 the the DET ijassa-713 113 7 total total ADJ ijassa-713 113 8 debt debt NOUN ijassa-713 113 9 of of ADP ijassa-713 113 10 the the DET ijassa-713 113 11 nation nation NOUN ijassa-713 113 12 by by ADP ijassa-713 113 13 summing sum VERB ijassa-713 113 14 the the DET ijassa-713 113 15 external external ADJ ijassa-713 113 16 debt debt NOUN ijassa-713 113 17 stock stock NOUN ijassa-713 113 18 ( ( PUNCT ijassa-713 113 19 federal federal ADJ ijassa-713 113 20 government government NOUN ijassa-713 113 21 and and CCONJ ijassa-713 113 22 state state NOUN ijassa-713 113 23 ) ) PUNCT ijassa-713 113 24 and and CCONJ ijassa-713 113 25 domestic domestic ADJ ijassa-713 113 26 debt debt NOUN ijassa-713 113 27 ( ( PUNCT ijassa-713 113 28 federal federal ADJ ijassa-713 113 29 government government NOUN ijassa-713 113 30 and and CCONJ ijassa-713 113 31 state state NOUN ijassa-713 113 32 ) ) PUNCT ijassa-713 113 33 together together ADV ijassa-713 113 34 . . PUNCT ijassa-713 114 1 the the DET ijassa-713 114 2 net net ADJ ijassa-713 114 3 worth worth NOUN ijassa-713 114 4 is be AUX ijassa-713 114 5 also also ADV ijassa-713 114 6 calculated calculate VERB ijassa-713 114 7 by by ADP ijassa-713 114 8 deducting deduct VERB ijassa-713 114 9 the the DET ijassa-713 114 10 debt debt NOUN ijassa-713 114 11 from from ADP ijassa-713 114 12 the the DET ijassa-713 114 13 gfcf gfcf NOUN ijassa-713 114 14 . . PUNCT ijassa-713 115 1 the the DET ijassa-713 115 2 cbn cbn PROPN ijassa-713 115 3 official official ADJ ijassa-713 115 4 exchange exchange NOUN ijassa-713 115 5 rate rate NOUN ijassa-713 115 6 of of ADP ijassa-713 115 7 π‘ˆπ‘†π· π‘ˆπ‘†π· NOUN ijassa-713 115 8 at at ADP ijassa-713 115 9 31st 31st NOUN ijassa-713 115 10 december december PROPN ijassa-713 115 11 of of ADP ijassa-713 115 12 each each DET ijassa-713 115 13 year year NOUN ijassa-713 115 14 is be AUX ijassa-713 115 15 used use VERB ijassa-713 115 16 while while SCONJ ijassa-713 115 17 current current ADJ ijassa-713 115 18 market market NOUN ijassa-713 115 19 prices price NOUN ijassa-713 115 20 from from ADP ijassa-713 115 21 the the DET ijassa-713 115 22 national national ADJ ijassa-713 115 23 account account NOUN ijassa-713 115 24 are be AUX ijassa-713 115 25 used use VERB ijassa-713 115 26 in in ADP ijassa-713 115 27 the the DET ijassa-713 115 28 computations computation NOUN ijassa-713 115 29 . . PUNCT ijassa-713 116 1 4.1 4.1 NUM ijassa-713 116 2 solution solution NOUN ijassa-713 116 3 to to ADP ijassa-713 116 4 the the DET ijassa-713 116 5 model model NOUN ijassa-713 116 6 here here ADV ijassa-713 116 7 , , PUNCT ijassa-713 116 8 the the DET ijassa-713 116 9 analytical analytical ADJ ijassa-713 116 10 and and CCONJ ijassa-713 116 11 numerical numerical ADJ ijassa-713 116 12 solutions solution NOUN ijassa-713 116 13 are be AUX ijassa-713 116 14 derived derive VERB ijassa-713 116 15 . . PUNCT ijassa-713 117 1 for for ADP ijassa-713 117 2 the the DET ijassa-713 117 3 analytic analytic ADJ ijassa-713 117 4 solution solution NOUN ijassa-713 117 5 , , PUNCT ijassa-713 117 6 the the DET ijassa-713 117 7 required require VERB ijassa-713 117 8 problem problem NOUN ijassa-713 117 9 under under ADP ijassa-713 117 10 consideration consideration NOUN ijassa-713 117 11 is be AUX ijassa-713 117 12 𝐽(πœ“ 𝐽(πœ“ NOUN ijassa-713 117 13 ) ) PUNCT ijassa-713 117 14 = = SYM ijassa-713 117 15 minπœ“πΈπΆ minπœ“πΈπΆ PROPN ijassa-713 117 16 [ [ PUNCT ijassa-713 117 17 ∫ ∫ PROPN ijassa-713 117 18 𝑑𝑛 𝑑𝑛 VERB ijassa-713 117 19 𝑑0 𝑑0 PROPN ijassa-713 117 20 1 1 NUM ijassa-713 117 21 πœ† πœ† NOUN ijassa-713 117 22 π‘’βˆ’πœ‚π‘‘(πœ“π‘‹(𝑑))πœ†π‘‘π‘‘ π‘’βˆ’πœ‚π‘‘(πœ“π‘‹(𝑑))πœ†π‘‘π‘‘ NOUN ijassa-713 117 23 ] ] X ijassa-713 117 24 subject subject NOUN ijassa-713 117 25 to to ADP ijassa-713 117 26 𝑑𝑋(𝑑 𝑑𝑋(𝑑 NUM ijassa-713 117 27 ) ) PUNCT ijassa-713 117 28 = = PUNCT ijassa-713 118 1 [ [ X ijassa-713 118 2 ( ( PUNCT ijassa-713 118 3 πœ… πœ… PRON ijassa-713 118 4 + + X ijassa-713 118 5 𝛽)πœ“ 𝛽)πœ“ ADJ ijassa-713 118 6 βˆ’ βˆ’ PROPN ijassa-713 118 7 ( ( PUNCT ijassa-713 118 8 πœ”(πœ“ πœ”(πœ“ PROPN ijassa-713 118 9 βˆ’ βˆ’ PROPN ijassa-713 118 10 1 1 NUM ijassa-713 118 11 ) ) PUNCT ijassa-713 118 12 + + CCONJ ijassa-713 118 13 πœ‡ πœ‡ ADP ijassa-713 118 14 + + X ijassa-713 118 15 𝑠 𝑠 INTJ ijassa-713 118 16 βˆ’ βˆ’ NOUN ijassa-713 118 17 𝑗 𝑗 INTJ ijassa-713 118 18 βˆ’ βˆ’ NOUN ijassa-713 118 19 𝑔)]𝑋(𝑑)𝑑𝑑 𝑔)]𝑋(𝑑)𝑑𝑑 ADJ ijassa-713 119 1 + + PROPN ijassa-713 119 2 [ [ X ijassa-713 119 3 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 119 4 + + CCONJ ijassa-713 119 5 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 119 6 βˆ’ βˆ’ NOUN ijassa-713 119 7 πœŽπ‘Ÿ(πœ“ πœŽπ‘Ÿ(πœ“ PUNCT ijassa-713 119 8 βˆ’ βˆ’ PROPN ijassa-713 119 9 1)]𝑋(𝑑)𝑑𝐢(𝑑 1)]𝑋(𝑑)𝑑𝐢(𝑑 NUM ijassa-713 119 10 ) ) PUNCT ijassa-713 119 11 with with ADP ijassa-713 119 12 𝛼-path 𝛼-path NOUN ijassa-713 119 13 equation equation NOUN ijassa-713 119 14 𝑑𝑋(𝑑)𝛼 𝑑𝑋(𝑑)𝛼 ADV ijassa-713 119 15 = = PUNCT ijassa-713 120 1 [ [ X ijassa-713 120 2 ( ( PUNCT ijassa-713 120 3 πœ… πœ… DET ijassa-713 120 4 + + X ijassa-713 120 5 𝛽)πœ“ 𝛽)πœ“ ADJ ijassa-713 120 6 βˆ’ βˆ’ PROPN ijassa-713 120 7 ( ( PUNCT ijassa-713 120 8 πœ”(πœ“ πœ”(πœ“ PROPN ijassa-713 120 9 βˆ’ βˆ’ PROPN ijassa-713 120 10 1 1 NUM ijassa-713 120 11 ) ) PUNCT ijassa-713 120 12 + + CCONJ ijassa-713 120 13 πœ‡ πœ‡ ADP ijassa-713 120 14 + + NOUN ijassa-713 120 15 β„Ž β„Ž PART ijassa-713 120 16 βˆ’ βˆ’ NOUN ijassa-713 120 17 𝑗 𝑗 INTJ ijassa-713 120 18 βˆ’ βˆ’ X ijassa-713 120 19 𝑔)]𝑋(𝑑)𝛼𝑑𝑑 𝑔)]𝑋(𝑑)𝛼𝑑𝑑 PROPN ijassa-713 120 20 + + CCONJ ijassa-713 120 21 |[πœ“πœŽπ‘ |[πœ“πœŽπ‘ ADJ ijassa-713 120 22 + + CCONJ ijassa-713 120 23 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 120 24 βˆ’ βˆ’ NOUN ijassa-713 120 25 πœŽπ‘Ÿ(πœ“ πœŽπ‘Ÿ(πœ“ PUNCT ijassa-713 120 26 βˆ’ βˆ’ PROPN ijassa-713 121 1 1)]𝑋(𝑑)𝛼|Ο†βˆ’1(𝛼)𝑑𝑑. 1)]𝑋(𝑑)𝛼|Ο†βˆ’1(𝛼)𝑑𝑑. NOUN ijassa-713 121 2 the the DET ijassa-713 121 3 analytical analytical ADJ ijassa-713 121 4 solution solution NOUN ijassa-713 121 5 to to ADP ijassa-713 121 6 the the DET ijassa-713 121 7 constraint constraint NOUN ijassa-713 121 8 is be AUX ijassa-713 121 9 t. t. NOUN ijassa-713 121 10 latunde latunde VERB ijassa-713 121 11 59 59 NUM ijassa-713 121 12 copyright copyright NOUN ijassa-713 121 13 Β© Β© PROPN ijassa-713 121 14 2019 2019 NUM ijassa-713 121 15 assa assa NOUN ijassa-713 121 16 . . PUNCT ijassa-713 122 1 adv adv PROPN ijassa-713 122 2 . . PUNCT ijassa-713 123 1 in in ADP ijassa-713 123 2 systems system NOUN ijassa-713 123 3 science science NOUN ijassa-713 123 4 and and CCONJ ijassa-713 123 5 appl appl NOUN ijassa-713 123 6 . . PUNCT ijassa-713 124 1 ( ( PUNCT ijassa-713 124 2 2019 2019 NUM ijassa-713 124 3 ) ) PUNCT ijassa-713 124 4 𝑋(𝑑 𝑋(𝑑 NUM ijassa-713 124 5 ) ) PUNCT ijassa-713 124 6 = = SYM ijassa-713 124 7 𝑋0exp([(πœ… 𝑋0exp([(πœ… NOUN ijassa-713 124 8 + + CCONJ ijassa-713 124 9 𝛽)πœ“ 𝛽)πœ“ ADJ ijassa-713 124 10 βˆ’ βˆ’ PROPN ijassa-713 124 11 ( ( PUNCT ijassa-713 124 12 πœ”(πœ“ πœ”(πœ“ PROPN ijassa-713 124 13 βˆ’ βˆ’ PROPN ijassa-713 124 14 1 1 NUM ijassa-713 124 15 ) ) PUNCT ijassa-713 124 16 + + CCONJ ijassa-713 124 17 πœ‡ πœ‡ ADP ijassa-713 124 18 + + X ijassa-713 124 19 𝑠 𝑠 INTJ ijassa-713 124 20 βˆ’ βˆ’ NOUN ijassa-713 124 21 𝑗 𝑗 INTJ ijassa-713 124 22 βˆ’ βˆ’ NOUN ijassa-713 124 23 𝑔)]𝑑 𝑔)]𝑑 NOUN ijassa-713 125 1 + + CCONJ ijassa-713 126 1 [ [ X ijassa-713 126 2 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 126 3 + + CCONJ ijassa-713 126 4 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 126 5 βˆ’ βˆ’ NOUN ijassa-713 126 6 πœŽπ‘Ÿ(πœ“ πœŽπ‘Ÿ(πœ“ PUNCT ijassa-713 126 7 βˆ’ βˆ’ PROPN ijassa-713 126 8 1)]𝐢(𝑑 1)]𝐢(𝑑 NUM ijassa-713 126 9 ) ) PUNCT ijassa-713 126 10 ) ) PUNCT ijassa-713 126 11 and and CCONJ ijassa-713 126 12 its its PRON ijassa-713 126 13 inverse inverse ADJ ijassa-713 126 14 uncertainty uncertainty NOUN ijassa-713 126 15 distribution distribution NOUN ijassa-713 126 16 is be AUX ijassa-713 126 17 ψ(𝑑)βˆ’1(𝛼 ψ(𝑑)βˆ’1(𝛼 NOUN ijassa-713 126 18 ) ) PUNCT ijassa-713 126 19 = = SYM ijassa-713 126 20 𝑋0exp([(πœ… 𝑋0exp([(πœ… NOUN ijassa-713 126 21 + + CCONJ ijassa-713 126 22 𝛽)πœ“ 𝛽)πœ“ ADJ ijassa-713 126 23 βˆ’ βˆ’ PROPN ijassa-713 126 24 ( ( PUNCT ijassa-713 126 25 πœ”(πœ“ πœ”(πœ“ PROPN ijassa-713 126 26 βˆ’ βˆ’ PROPN ijassa-713 126 27 1 1 NUM ijassa-713 126 28 ) ) PUNCT ijassa-713 126 29 + + CCONJ ijassa-713 127 1 πœ‡ πœ‡ ADP ijassa-713 127 2 + + X ijassa-713 127 3 𝑠 𝑠 INTJ ijassa-713 127 4 βˆ’ βˆ’ NOUN ijassa-713 127 5 𝑗 𝑗 INTJ ijassa-713 127 6 βˆ’ βˆ’ NOUN ijassa-713 127 7 𝑔)]𝑑 𝑔)]𝑑 NOUN ijassa-713 127 8 + + CCONJ ijassa-713 128 1 [ [ X ijassa-713 128 2 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 128 3 + + CCONJ ijassa-713 128 4 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 128 5 βˆ’ βˆ’ NOUN ijassa-713 128 6 πœŽπ‘Ÿ(πœ“ πœŽπ‘Ÿ(πœ“ PUNCT ijassa-713 128 7 βˆ’ βˆ’ PROPN ijassa-713 128 8 1)]π‘‘βˆš3 1)]π‘‘βˆš3 NUM ijassa-713 128 9 πœ‹ πœ‹ NOUN ijassa-713 128 10 ln ln NOUN ijassa-713 128 11 𝛼 𝛼 PROPN ijassa-713 128 12 1 1 NUM ijassa-713 128 13 βˆ’ βˆ’ PROPN ijassa-713 128 14 𝛼 𝛼 NOUN ijassa-713 128 15 ) ) PUNCT ijassa-713 128 16 hence hence ADV ijassa-713 128 17 , , PUNCT ijassa-713 128 18 by by ADP ijassa-713 128 19 theorem theorem NOUN ijassa-713 128 20 2.1 2.1 NUM ijassa-713 128 21 , , PUNCT ijassa-713 128 22 ψ(𝑑)βˆ’1(𝛼 ψ(𝑑)βˆ’1(𝛼 NOUN ijassa-713 128 23 ) ) PUNCT ijassa-713 128 24 = = SYM ijassa-713 128 25 𝐸(𝑋(𝑑)𝛼 𝐸(𝑋(𝑑)𝛼 NOUN ijassa-713 128 26 ) ) PUNCT ijassa-713 128 27 numerical numerical ADJ ijassa-713 128 28 solutions solution NOUN ijassa-713 128 29 are be AUX ijassa-713 128 30 presented present VERB ijassa-713 128 31 via via ADP ijassa-713 128 32 trapezoidal trapezoidal ADJ ijassa-713 128 33 rule rule NOUN ijassa-713 128 34 for for ADP ijassa-713 128 35 the the DET ijassa-713 128 36 objective objective ADJ ijassa-713 128 37 functional functional ADJ ijassa-713 128 38 and and CCONJ ijassa-713 128 39 , , PUNCT ijassa-713 128 40 euler euler NOUN ijassa-713 128 41 method method NOUN ijassa-713 128 42 and and CCONJ ijassa-713 128 43 fourth fourth ADJ ijassa-713 128 44 order order NOUN ijassa-713 128 45 runge runge NOUN ijassa-713 128 46 - - PUNCT ijassa-713 128 47 kutta kutta NOUN ijassa-713 128 48 method method NOUN ijassa-713 128 49 for for ADP ijassa-713 128 50 solving solve VERB ijassa-713 128 51 uncertain uncertain ADJ ijassa-713 128 52 differential differential ADJ ijassa-713 128 53 equations equation NOUN ijassa-713 128 54 due due ADP ijassa-713 128 55 to to ADP ijassa-713 128 56 its its PRON ijassa-713 128 57 ability ability NOUN ijassa-713 128 58 to to PART ijassa-713 128 59 yield yield VERB ijassa-713 128 60 more more ADV ijassa-713 128 61 precise precise ADJ ijassa-713 128 62 outcomes outcome NOUN ijassa-713 128 63 than than ADP ijassa-713 128 64 other other ADJ ijassa-713 128 65 methods method NOUN ijassa-713 128 66 for for ADP ijassa-713 128 67 the the DET ijassa-713 128 68 constraints constraint NOUN ijassa-713 128 69 , , PUNCT ijassa-713 128 70 [ [ X ijassa-713 128 71 17 17 NUM ijassa-713 128 72 ] ] PUNCT ijassa-713 128 73 . . PUNCT ijassa-713 129 1 trapezoidal trapezoidal ADJ ijassa-713 129 2 method method NOUN ijassa-713 129 3 : : PUNCT ijassa-713 129 4 ∫ ∫ PROPN ijassa-713 129 5 𝑏 𝑏 PROPN ijassa-713 129 6 π‘Ž π‘Ž PROPN ijassa-713 129 7 𝑓(π‘₯)𝑑π‘₯ 𝑓(π‘₯)𝑑π‘₯ NOUN ijassa-713 129 8 = = PUNCT ijassa-713 129 9 β„Ž β„Ž X ijassa-713 129 10 2 2 NUM ijassa-713 129 11 ( ( PUNCT ijassa-713 129 12 𝑓0 𝑓0 NOUN ijassa-713 129 13 + + CCONJ ijassa-713 129 14 2𝑓1 2𝑓1 NUM ijassa-713 129 15 + + CCONJ ijassa-713 129 16 2𝑓2 2𝑓2 NUM ijassa-713 130 1 + + CCONJ ijassa-713 130 2 β‹― β‹― X ijassa-713 130 3 + + CCONJ ijassa-713 130 4 2π‘“π‘›βˆ’1 2π‘“π‘›βˆ’1 NUM ijassa-713 130 5 + + CCONJ ijassa-713 130 6 𝑓𝑛 𝑓𝑛 NOUN ijassa-713 130 7 ) ) PUNCT ijassa-713 130 8 = = SYM ijassa-713 130 9 β„Ž β„Ž PROPN ijassa-713 130 10 ( ( PUNCT ijassa-713 130 11 𝑓0 𝑓0 PROPN ijassa-713 131 1 + + CCONJ ijassa-713 131 2 𝑓𝑛 𝑓𝑛 NOUN ijassa-713 131 3 2 2 NUM ijassa-713 131 4 + + CCONJ ijassa-713 131 5 βˆ‘ βˆ‘ PROPN ijassa-713 131 6 π‘›βˆ’1 π‘›βˆ’1 PROPN ijassa-713 131 7 𝑖=1 𝑖=1 PROPN ijassa-713 131 8 𝑓𝑖 𝑓𝑖 PROPN ijassa-713 131 9 ) ) PUNCT ijassa-713 131 10 , , PUNCT ijassa-713 131 11 where where SCONJ ijassa-713 131 12 𝑓(π‘₯π‘˜ 𝑓(π‘₯π‘˜ ADJ ijassa-713 131 13 ) ) PUNCT ijassa-713 131 14 ≑ ≑ PROPN ijassa-713 131 15 π‘“π‘˜ π‘“π‘˜ ADP ijassa-713 131 16 the the DET ijassa-713 131 17 runge runge NOUN ijassa-713 131 18 - - PUNCT ijassa-713 131 19 kutta kutta NOUN ijassa-713 131 20 method method NOUN ijassa-713 131 21 for for ADP ijassa-713 131 22 solving solve VERB ijassa-713 131 23 uncertain uncertain ADJ ijassa-713 131 24 differential differential ADJ ijassa-713 131 25 equations equation NOUN ijassa-713 131 26 was be AUX ijassa-713 131 27 designed design VERB ijassa-713 131 28 in in ADP ijassa-713 131 29 [ [ X ijassa-713 131 30 17 17 NUM ijassa-713 131 31 ] ] PUNCT ijassa-713 131 32 with with ADP ijassa-713 131 33 respect respect NOUN ijassa-713 131 34 to to ADP ijassa-713 131 35 the the DET ijassa-713 131 36 following follow VERB ijassa-713 131 37 definition definition NOUN ijassa-713 131 38 and and CCONJ ijassa-713 131 39 theorems theorem NOUN ijassa-713 131 40 . . PUNCT ijassa-713 131 41 runge runge NOUN ijassa-713 131 42 - - PUNCT ijassa-713 131 43 kutta kutta NOUN ijassa-713 131 44 method method NOUN ijassa-713 131 45 is be AUX ijassa-713 131 46 an an DET ijassa-713 131 47 effective effective ADJ ijassa-713 131 48 method method NOUN ijassa-713 131 49 for for ADP ijassa-713 131 50 solving solve VERB ijassa-713 131 51 ordinary ordinary ADJ ijassa-713 131 52 differential differential ADJ ijassa-713 131 53 equations equation NOUN ijassa-713 131 54 . . PUNCT ijassa-713 132 1 the the DET ijassa-713 132 2 generally generally ADV ijassa-713 132 3 used use VERB ijassa-713 132 4 runge runge NOUN ijassa-713 132 5 - - PUNCT ijassa-713 132 6 kutta kutta NOUN ijassa-713 132 7 formula formula NOUN ijassa-713 132 8 is be AUX ijassa-713 132 9 a a DET ijassa-713 132 10 fourth fourth ADJ ijassa-713 132 11 - - PUNCT ijassa-713 132 12 order order NOUN ijassa-713 132 13 formula formula NOUN ijassa-713 132 14 . . PUNCT ijassa-713 133 1 it it PRON ijassa-713 133 2 should should AUX ijassa-713 133 3 be be AUX ijassa-713 133 4 noted note VERB ijassa-713 133 5 that that SCONJ ijassa-713 133 6 there there PRON ijassa-713 133 7 is be VERB ijassa-713 133 8 a a DET ijassa-713 133 9 wide wide ADJ ijassa-713 133 10 range range NOUN ijassa-713 133 11 of of ADP ijassa-713 133 12 fourth fourth ADJ ijassa-713 133 13 - - PUNCT ijassa-713 133 14 order order NOUN ijassa-713 133 15 schemes scheme NOUN ijassa-713 133 16 and and CCONJ ijassa-713 133 17 here here ADV ijassa-713 133 18 , , PUNCT ijassa-713 133 19 just just ADV ijassa-713 133 20 one one NUM ijassa-713 133 21 common common ADJ ijassa-713 133 22 structure structure NOUN ijassa-713 133 23 is be AUX ijassa-713 133 24 exhibited exhibit VERB ijassa-713 133 25 . . PUNCT ijassa-713 134 1 for for ADP ijassa-713 134 2 an an DET ijassa-713 134 3 ordinary ordinary ADJ ijassa-713 134 4 differential differential ADJ ijassa-713 134 5 equation equation NOUN ijassa-713 134 6 with with ADP ijassa-713 134 7 initial initial ADJ ijassa-713 134 8 value value NOUN ijassa-713 134 9 𝑋0 𝑋0 NOUN ijassa-713 134 10 𝑑𝑋(𝑑 𝑑𝑋(𝑑 PROPN ijassa-713 134 11 ) ) PUNCT ijassa-713 134 12 = = PUNCT ijassa-713 134 13 𝐹(𝑑 𝐹(𝑑 NOUN ijassa-713 134 14 , , PUNCT ijassa-713 134 15 𝑋(𝑑))𝑑𝑑. 𝑋(𝑑))𝑑𝑑. VERB ijassa-713 134 16 the the DET ijassa-713 134 17 scheme scheme NOUN ijassa-713 134 18 uses use VERB ijassa-713 134 19 the the DET ijassa-713 134 20 following follow VERB ijassa-713 134 21 formula formula NOUN ijassa-713 134 22 𝑋(𝑑𝑛+1 𝑋(𝑑𝑛+1 NOUN ijassa-713 134 23 ) ) PUNCT ijassa-713 134 24 = = SYM ijassa-713 134 25 𝑋(𝑑𝑛 𝑋(𝑑𝑛 NOUN ijassa-713 134 26 ) ) PUNCT ijassa-713 135 1 + + CCONJ ijassa-713 135 2 1 1 NUM ijassa-713 135 3 6 6 NUM ijassa-713 135 4 ( ( PUNCT ijassa-713 135 5 π‘˜1 π‘˜1 PROPN ijassa-713 135 6 + + CCONJ ijassa-713 135 7 2π‘˜2 2π‘˜2 NUM ijassa-713 135 8 + + CCONJ ijassa-713 135 9 2π‘˜3 2π‘˜3 NUM ijassa-713 135 10 + + NUM ijassa-713 135 11 π‘˜4 π‘˜4 PROPN ijassa-713 135 12 ) ) PUNCT ijassa-713 135 13 where where SCONJ ijassa-713 135 14 π‘˜1 π‘˜1 ADJ ijassa-713 135 15 = = SYM ijassa-713 135 16 β„ŽπΉ(𝑑𝑛 β„ŽπΉ(𝑑𝑛 X ijassa-713 135 17 , , PUNCT ijassa-713 135 18 𝑋𝑛 𝑋𝑛 PROPN ijassa-713 135 19 ) ) PUNCT ijassa-713 135 20 , , PUNCT ijassa-713 135 21 π‘˜2 π‘˜2 NOUN ijassa-713 135 22 = = PUNCT ijassa-713 135 23 β„ŽπΉ(𝑑𝑛 β„ŽπΉ(𝑑𝑛 PROPN ijassa-713 135 24 + + CCONJ ijassa-713 135 25 β„Ž β„Ž X ijassa-713 135 26 2 2 NUM ijassa-713 135 27 , , PUNCT ijassa-713 135 28 𝑋𝑛 𝑋𝑛 NOUN ijassa-713 135 29 + + NOUN ijassa-713 135 30 1 1 NUM ijassa-713 135 31 2 2 NUM ijassa-713 135 32 π‘˜1 π‘˜1 NOUN ijassa-713 135 33 ) ) PUNCT ijassa-713 135 34 , , PUNCT ijassa-713 135 35 π‘˜3 π‘˜3 PROPN ijassa-713 135 36 = = SYM ijassa-713 135 37 β„ŽπΉ(𝑑𝑛 β„ŽπΉ(𝑑𝑛 NOUN ijassa-713 135 38 + + CCONJ ijassa-713 135 39 β„Ž β„Ž X ijassa-713 135 40 2 2 NUM ijassa-713 135 41 , , PUNCT ijassa-713 135 42 𝑋𝑛 𝑋𝑛 NOUN ijassa-713 135 43 + + NOUN ijassa-713 135 44 1 1 NUM ijassa-713 135 45 2 2 NUM ijassa-713 135 46 π‘˜2 π‘˜2 NOUN ijassa-713 135 47 ) ) PUNCT ijassa-713 135 48 , , PUNCT ijassa-713 135 49 π‘˜4 π‘˜4 PROPN ijassa-713 135 50 = = SYM ijassa-713 135 51 β„ŽπΉ(𝑑𝑛 β„ŽπΉ(𝑑𝑛 PROPN ijassa-713 135 52 + + CCONJ ijassa-713 135 53 β„Ž β„Ž NOUN ijassa-713 135 54 , , PUNCT ijassa-713 135 55 𝑋𝑛 𝑋𝑛 PROPN ijassa-713 135 56 + + NUM ijassa-713 135 57 π‘˜3 π‘˜3 PROPN ijassa-713 135 58 ) ) PUNCT ijassa-713 135 59 and and CCONJ ijassa-713 135 60 β„Ž β„Ž PROPN ijassa-713 135 61 is be AUX ijassa-713 135 62 the the DET ijassa-713 135 63 step step NOUN ijassa-713 135 64 size size NOUN ijassa-713 135 65 which which PRON ijassa-713 135 66 is be AUX ijassa-713 135 67 assumed assume VERB ijassa-713 135 68 to to PART ijassa-713 135 69 be be AUX ijassa-713 135 70 constant constant ADJ ijassa-713 135 71 for for ADP ijassa-713 135 72 all all DET ijassa-713 135 73 steps step NOUN ijassa-713 135 74 . . PUNCT ijassa-713 136 1 however however ADV ijassa-713 136 2 , , PUNCT ijassa-713 136 3 based base VERB ijassa-713 136 4 on on ADP ijassa-713 136 5 theorem theorem ADJ ijassa-713 136 6 2.4 2.4 NUM ijassa-713 136 7 , , PUNCT ijassa-713 136 8 a a DET ijassa-713 136 9 runge runge NOUN ijassa-713 136 10 - - PUNCT ijassa-713 136 11 kutta kutta NOUN ijassa-713 136 12 method method NOUN ijassa-713 136 13 for for ADP ijassa-713 136 14 uncertain uncertain ADJ ijassa-713 136 15 differential differential ADJ ijassa-713 136 16 equations equation NOUN ijassa-713 136 17 was be AUX ijassa-713 136 18 designed design VERB ijassa-713 136 19 as as ADP ijassa-713 136 20 𝑋𝑖+1 𝑋𝑖+1 X ijassa-713 136 21 𝛼 𝛼 NOUN ijassa-713 136 22 = = PUNCT ijassa-713 136 23 𝑋𝑖 𝑋𝑖 NOUN ijassa-713 136 24 𝛼 𝛼 NOUN ijassa-713 136 25 + + NOUN ijassa-713 136 26 1 1 NUM ijassa-713 136 27 6 6 NUM ijassa-713 136 28 ( ( PUNCT ijassa-713 136 29 π‘˜1 π‘˜1 PROPN ijassa-713 136 30 + + CCONJ ijassa-713 136 31 2π‘˜2 2π‘˜2 NUM ijassa-713 136 32 + + CCONJ ijassa-713 136 33 2π‘˜3 2π‘˜3 NUM ijassa-713 136 34 + + NUM ijassa-713 136 35 π‘˜4 π‘˜4 PROPN ijassa-713 136 36 ) ) PUNCT ijassa-713 136 37 where where SCONJ ijassa-713 136 38 60 60 NUM ijassa-713 136 39 optimal optimal ADJ ijassa-713 136 40 values value NOUN ijassa-713 136 41 in in ADP ijassa-713 136 42 uncertin uncertin PROPN ijassa-713 136 43 optimal optimal ADJ ijassa-713 136 44 control control NOUN ijassa-713 136 45 model model NOUN ijassa-713 136 46 copyright copyright NOUN ijassa-713 136 47 Β© Β© PROPN ijassa-713 136 48 2019 2019 NUM ijassa-713 136 49 assa assa PROPN ijassa-713 136 50 adv adv PROPN ijassa-713 136 51 . . PUNCT ijassa-713 137 1 in in ADP ijassa-713 137 2 systems system NOUN ijassa-713 137 3 science science NOUN ijassa-713 137 4 and and CCONJ ijassa-713 137 5 appl appl NOUN ijassa-713 137 6 . . PUNCT ijassa-713 138 1 ( ( PUNCT ijassa-713 138 2 2019 2019 NUM ijassa-713 138 3 ) ) PUNCT ijassa-713 138 4 π‘˜1 π‘˜1 NOUN ijassa-713 138 5 = = PUNCT ijassa-713 138 6 β„Ž(𝑓(𝑑𝑖 β„Ž(𝑓(𝑑𝑖 PROPN ijassa-713 138 7 , , PUNCT ijassa-713 138 8 𝑋𝑖 𝑋𝑖 PROPN ijassa-713 138 9 𝛼 𝛼 PROPN ijassa-713 138 10 ) ) PUNCT ijassa-713 138 11 + + CCONJ ijassa-713 139 1 |𝑔(𝑑𝑖 |𝑔(𝑑𝑖 NOUN ijassa-713 139 2 , , PUNCT ijassa-713 139 3 𝑋𝑖 𝑋𝑖 PROPN ijassa-713 139 4 𝛼 𝛼 NOUN ijassa-713 139 5 ) ) PUNCT ijassa-713 139 6 |Ο†βˆ’1(𝛼 |Ο†βˆ’1(𝛼 NOUN ijassa-713 139 7 ) ) PUNCT ijassa-713 139 8 ) ) PUNCT ijassa-713 139 9 , , PUNCT ijassa-713 139 10 π‘˜2 π‘˜2 PROPN ijassa-713 139 11 = = PUNCT ijassa-713 139 12 β„Ž(𝑓(𝑑𝑖 β„Ž(𝑓(𝑑𝑖 PROPN ijassa-713 139 13 + + CCONJ ijassa-713 139 14 β„Ž β„Ž X ijassa-713 139 15 2 2 NUM ijassa-713 139 16 , , PUNCT ijassa-713 139 17 𝑋𝑖 𝑋𝑖 PROPN ijassa-713 139 18 𝛼 𝛼 NOUN ijassa-713 139 19 + + NOUN ijassa-713 139 20 1 1 NUM ijassa-713 139 21 2 2 NUM ijassa-713 139 22 π‘˜1 π‘˜1 NOUN ijassa-713 139 23 ) ) PUNCT ijassa-713 140 1 + + CCONJ ijassa-713 140 2 |𝑔(𝑑𝑖 |𝑔(𝑑𝑖 NOUN ijassa-713 140 3 + + CCONJ ijassa-713 140 4 β„Ž β„Ž X ijassa-713 140 5 2 2 NUM ijassa-713 140 6 , , PUNCT ijassa-713 140 7 𝑋𝑖 𝑋𝑖 PROPN ijassa-713 140 8 𝛼 𝛼 NOUN ijassa-713 140 9 + + NOUN ijassa-713 140 10 1 1 NUM ijassa-713 140 11 2 2 NUM ijassa-713 140 12 π‘˜1)|Ο†βˆ’1(𝛼 π‘˜1)|Ο†βˆ’1(𝛼 NOUN ijassa-713 140 13 ) ) PUNCT ijassa-713 140 14 ) ) PUNCT ijassa-713 140 15 , , PUNCT ijassa-713 140 16 π‘˜3 π‘˜3 PROPN ijassa-713 140 17 = = SYM ijassa-713 140 18 β„Ž(𝑓(𝑑𝑖 β„Ž(𝑓(𝑑𝑖 PROPN ijassa-713 140 19 + + CCONJ ijassa-713 140 20 β„Ž β„Ž X ijassa-713 140 21 2 2 NUM ijassa-713 140 22 , , PUNCT ijassa-713 140 23 𝑋𝑖 𝑋𝑖 PROPN ijassa-713 140 24 𝛼 𝛼 NOUN ijassa-713 140 25 + + NOUN ijassa-713 140 26 1 1 NUM ijassa-713 140 27 2 2 NUM ijassa-713 140 28 π‘˜2 π‘˜2 NOUN ijassa-713 140 29 ) ) PUNCT ijassa-713 141 1 + + CCONJ ijassa-713 141 2 |𝑔(𝑑𝑖 |𝑔(𝑑𝑖 NOUN ijassa-713 141 3 + + CCONJ ijassa-713 141 4 β„Ž β„Ž X ijassa-713 141 5 2 2 NUM ijassa-713 141 6 , , PUNCT ijassa-713 141 7 𝑋𝑖 𝑋𝑖 PROPN ijassa-713 141 8 𝛼 𝛼 NOUN ijassa-713 141 9 + + NOUN ijassa-713 141 10 1 1 NUM ijassa-713 141 11 2 2 NUM ijassa-713 141 12 π‘˜2)|Ο†βˆ’1(𝛼 π‘˜2)|Ο†βˆ’1(𝛼 NOUN ijassa-713 141 13 ) ) PUNCT ijassa-713 141 14 ) ) PUNCT ijassa-713 141 15 , , PUNCT ijassa-713 141 16 π‘˜4 π‘˜4 PROPN ijassa-713 141 17 = = SYM ijassa-713 141 18 β„Ž(𝑓(𝑑𝑖 β„Ž(𝑓(𝑑𝑖 PROPN ijassa-713 141 19 + + X ijassa-713 141 20 β„Ž β„Ž PROPN ijassa-713 141 21 , , PUNCT ijassa-713 141 22 𝑋𝑖 𝑋𝑖 PROPN ijassa-713 141 23 𝛼 𝛼 NOUN ijassa-713 141 24 + + X ijassa-713 141 25 π‘˜3 π‘˜3 PROPN ijassa-713 141 26 ) ) PUNCT ijassa-713 142 1 + + CCONJ ijassa-713 142 2 |𝑔(𝑑𝑖 |𝑔(𝑑𝑖 NOUN ijassa-713 142 3 + + CCONJ ijassa-713 142 4 β„Ž β„Ž PROPN ijassa-713 142 5 , , PUNCT ijassa-713 142 6 𝑋𝑖 𝑋𝑖 NOUN ijassa-713 142 7 𝛼 𝛼 NOUN ijassa-713 142 8 + + X ijassa-713 142 9 π‘˜3)|Ο†βˆ’1(𝛼 π‘˜3)|Ο†βˆ’1(𝛼 NOUN ijassa-713 142 10 ) ) PUNCT ijassa-713 142 11 ) ) PUNCT ijassa-713 142 12 . . PUNCT ijassa-713 143 1 for for ADP ijassa-713 143 2 the the DET ijassa-713 143 3 proposed propose VERB ijassa-713 143 4 optimal optimal ADJ ijassa-713 143 5 control control NOUN ijassa-713 143 6 model model NOUN ijassa-713 143 7 of of ADP ijassa-713 143 8 net net ADJ ijassa-713 143 9 risky risky ADJ ijassa-713 143 10 capital capital NOUN ijassa-713 143 11 asset asset NOUN ijassa-713 143 12 with with ADP ijassa-713 143 13 an an DET ijassa-713 143 14 uncertain uncertain ADJ ijassa-713 143 15 differential differential ADJ ijassa-713 143 16 equation equation NOUN ijassa-713 143 17 𝑑𝑋(𝑑 𝑑𝑋(𝑑 PROPN ijassa-713 143 18 ) ) PUNCT ijassa-713 143 19 = = PUNCT ijassa-713 144 1 [ [ X ijassa-713 144 2 ( ( PUNCT ijassa-713 144 3 πœ… πœ… PRON ijassa-713 144 4 + + X ijassa-713 144 5 𝛽)πœ“ 𝛽)πœ“ ADJ ijassa-713 144 6 βˆ’ βˆ’ PROPN ijassa-713 144 7 ( ( PUNCT ijassa-713 144 8 πœ”(πœ“ πœ”(πœ“ PROPN ijassa-713 144 9 βˆ’ βˆ’ PROPN ijassa-713 144 10 1 1 NUM ijassa-713 144 11 ) ) PUNCT ijassa-713 144 12 + + CCONJ ijassa-713 144 13 πœ‡ πœ‡ ADP ijassa-713 144 14 + + NOUN ijassa-713 144 15 β„Ž β„Ž PART ijassa-713 144 16 βˆ’ βˆ’ NOUN ijassa-713 144 17 𝑗 𝑗 INTJ ijassa-713 144 18 βˆ’ βˆ’ NOUN ijassa-713 144 19 𝑔)]𝑋(𝑑)𝑑𝑑 𝑔)]𝑋(𝑑)𝑑𝑑 ADJ ijassa-713 144 20 + + CCONJ ijassa-713 145 1 [ [ X ijassa-713 145 2 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 145 3 + + CCONJ ijassa-713 145 4 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 145 5 βˆ’ βˆ’ NOUN ijassa-713 145 6 πœŽπ‘Ÿ(πœ“ πœŽπ‘Ÿ(πœ“ PUNCT ijassa-713 145 7 βˆ’ βˆ’ PROPN ijassa-713 145 8 1)]𝑋(𝑑)𝑑𝐢(𝑑 1)]𝑋(𝑑)𝑑𝐢(𝑑 NUM ijassa-713 145 9 ) ) PUNCT ijassa-713 145 10 with with ADP ijassa-713 145 11 initial initial ADJ ijassa-713 145 12 value value NOUN ijassa-713 145 13 𝑋0 𝑋0 NOUN ijassa-713 145 14 and and CCONJ ijassa-713 145 15 its its PRON ijassa-713 145 16 𝛼-path 𝛼-path NOUN ijassa-713 145 17 equation equation NOUN ijassa-713 145 18 . . PUNCT ijassa-713 146 1 i.e. i.e. X ijassa-713 146 2 , , PUNCT ijassa-713 146 3 𝑑𝑋(𝑑)𝛼 𝑑𝑋(𝑑)𝛼 ADV ijassa-713 146 4 = = PUNCT ijassa-713 147 1 [ [ X ijassa-713 147 2 ( ( PUNCT ijassa-713 147 3 πœ… πœ… PRON ijassa-713 147 4 + + X ijassa-713 147 5 𝛽)πœ“ 𝛽)πœ“ ADJ ijassa-713 147 6 βˆ’ βˆ’ PROPN ijassa-713 147 7 ( ( PUNCT ijassa-713 147 8 πœ”(πœ“ πœ”(πœ“ PROPN ijassa-713 147 9 βˆ’ βˆ’ PROPN ijassa-713 147 10 1 1 NUM ijassa-713 147 11 ) ) PUNCT ijassa-713 147 12 + + CCONJ ijassa-713 147 13 πœ‡ πœ‡ ADP ijassa-713 147 14 + + NOUN ijassa-713 147 15 β„Ž β„Ž PART ijassa-713 147 16 βˆ’ βˆ’ NOUN ijassa-713 147 17 𝑗 𝑗 INTJ ijassa-713 147 18 βˆ’ βˆ’ X ijassa-713 147 19 𝑔)]𝑋(𝑑)𝛼𝑑𝑑 𝑔)]𝑋(𝑑)𝛼𝑑𝑑 PROPN ijassa-713 147 20 + + ADJ ijassa-713 147 21 |[πœ“πœŽπ‘ |[πœ“πœŽπ‘ ADJ ijassa-713 147 22 + + CCONJ ijassa-713 147 23 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 147 24 βˆ’ βˆ’ NOUN ijassa-713 147 25 πœŽπ‘Ÿ(πœ“ πœŽπ‘Ÿ(πœ“ PUNCT ijassa-713 147 26 βˆ’ βˆ’ PROPN ijassa-713 147 27 1)]𝑋(𝑑)𝛼|Ο†βˆ’1(𝛼)𝑑𝑑 1)]𝑋(𝑑)𝛼|Ο†βˆ’1(𝛼)𝑑𝑑 NUM ijassa-713 147 28 , , PUNCT ijassa-713 147 29 this this PRON ijassa-713 147 30 is be AUX ijassa-713 147 31 solved solve VERB ijassa-713 147 32 using use VERB ijassa-713 147 33 the the DET ijassa-713 147 34 algorithm algorithm NOUN ijassa-713 147 35 below below ADV ijassa-713 147 36 . . PUNCT ijassa-713 148 1 4.2 4.2 NUM ijassa-713 148 2 . . PUNCT ijassa-713 148 3 algorithm algorithm NOUN ijassa-713 148 4 4.1 4.1 NUM ijassa-713 148 5 : : PUNCT ijassa-713 148 6 runge runge NOUN ijassa-713 148 7 - - PUNCT ijassa-713 148 8 kutta kutta NOUN ijassa-713 148 9 method method NOUN ijassa-713 148 10 for for ADP ijassa-713 148 11 solving solve VERB ijassa-713 148 12 the the DET ijassa-713 148 13 model model NOUN ijassa-713 148 14 step step NOUN ijassa-713 148 15 1 1 NUM ijassa-713 148 16 . . PUNCT ijassa-713 149 1 given give VERB ijassa-713 149 2 time time NOUN ijassa-713 149 3 interval interval NOUN ijassa-713 149 4 𝑑 𝑑 PROPN ijassa-713 149 5 , , PUNCT ijassa-713 149 6 [ [ X ijassa-713 149 7 π‘Ž π‘Ž X ijassa-713 149 8 , , PUNCT ijassa-713 149 9 𝑏 𝑏 NOUN ijassa-713 149 10 ] ] X ijassa-713 149 11 , , PUNCT ijassa-713 149 12 iteration iteration NOUN ijassa-713 149 13 number number NOUN ijassa-713 149 14 𝑁 𝑁 PROPN ijassa-713 149 15 , , PUNCT ijassa-713 149 16 step step NOUN ijassa-713 149 17 length length NOUN ijassa-713 149 18 β„Ž β„Ž X ijassa-713 149 19 = = SYM ijassa-713 149 20 π‘βˆ’π‘Ž π‘βˆ’π‘Ž PROPN ijassa-713 149 21 𝑁 𝑁 PROPN ijassa-713 149 22 . . PUNCT ijassa-713 149 23 set set VERB ijassa-713 149 24 𝑑𝑖 𝑑𝑖 NOUN ijassa-713 149 25 = = PUNCT ijassa-713 149 26 π‘Ž π‘Ž PROPN ijassa-713 149 27 + + NOUN ijassa-713 149 28 π‘–β„Ž π‘–β„Ž ADJ ijassa-713 149 29 , , PUNCT ijassa-713 149 30 𝑖 𝑖 NOUN ijassa-713 149 31 = = SYM ijassa-713 149 32 0,1 0,1 NUM ijassa-713 149 33 , , PUNCT ijassa-713 149 34 β‹― β‹― VERB ijassa-713 149 35 , , PUNCT ijassa-713 149 36 𝑁 𝑁 PROPN ijassa-713 149 37 and and CCONJ ijassa-713 149 38 𝛼 𝛼 ADJ ijassa-713 149 39 > > X ijassa-713 149 40 0 0 X ijassa-713 149 41 . . PUNCT ijassa-713 149 42 step step NOUN ijassa-713 149 43 2 2 NUM ijassa-713 149 44 . . X ijassa-713 149 45 compute compute VERB ijassa-713 149 46 the the DET ijassa-713 149 47 corresponding corresponding ADJ ijassa-713 149 48 differential differential ADJ ijassa-713 149 49 equation equation NOUN ijassa-713 149 50 𝑑𝑋(𝑑)𝛼 𝑑𝑋(𝑑)𝛼 ADV ijassa-713 149 51 = = PUNCT ijassa-713 150 1 [ [ X ijassa-713 150 2 ( ( PUNCT ijassa-713 150 3 πœ… πœ… DET ijassa-713 150 4 + + X ijassa-713 150 5 𝛽)πœ“ 𝛽)πœ“ ADJ ijassa-713 150 6 βˆ’ βˆ’ PROPN ijassa-713 150 7 ( ( PUNCT ijassa-713 150 8 πœ”(πœ“ πœ”(πœ“ PROPN ijassa-713 150 9 βˆ’ βˆ’ PROPN ijassa-713 150 10 1 1 NUM ijassa-713 150 11 ) ) PUNCT ijassa-713 150 12 + + CCONJ ijassa-713 150 13 πœ‡ πœ‡ ADP ijassa-713 150 14 + + X ijassa-713 150 15 𝑠 𝑠 INTJ ijassa-713 150 16 βˆ’ βˆ’ NOUN ijassa-713 150 17 𝑗 𝑗 INTJ ijassa-713 150 18 βˆ’ βˆ’ X ijassa-713 151 1 𝑔)]𝑋(𝑑)𝛼𝑑𝑑 𝑔)]𝑋(𝑑)𝛼𝑑𝑑 PROPN ijassa-713 151 2 + + ADJ ijassa-713 151 3 |[πœ“πœŽπ‘ |[πœ“πœŽπ‘ ADJ ijassa-713 151 4 + + CCONJ ijassa-713 151 5 πœ“πœŽπ‘ πœ“πœŽπ‘ NOUN ijassa-713 151 6 βˆ’ βˆ’ NOUN ijassa-713 151 7 πœŽπ‘Ÿ(πœ“ πœŽπ‘Ÿ(πœ“ PUNCT ijassa-713 151 8 βˆ’ βˆ’ PROPN ijassa-713 151 9 1)]𝑋(𝑑)𝛼| 1)]𝑋(𝑑)𝛼| PROPN ijassa-713 151 10 𝜎√3 𝜎√3 PROPN ijassa-713 151 11 πœ‹ πœ‹ X ijassa-713 151 12 ln ln NOUN ijassa-713 151 13 𝛼 𝛼 PROPN ijassa-713 151 14 1βˆ’π›Ό 1βˆ’π›Ό NUM ijassa-713 151 15 𝑑𝑑 𝑑𝑑 ADP ijassa-713 151 16 , , PUNCT ijassa-713 151 17 𝑋0 𝑋0 NOUN ijassa-713 151 18 𝛼 𝛼 NOUN ijassa-713 151 19 = = NOUN ijassa-713 151 20 𝑋0 𝑋0 PROPN ijassa-713 151 21 , , PUNCT ijassa-713 151 22 with with ADP ijassa-713 151 23 the the DET ijassa-713 151 24 runge runge NOUN ijassa-713 151 25 - - PUNCT ijassa-713 151 26 kutta kutta NOUN ijassa-713 151 27 method method NOUN ijassa-713 151 28 for for ADP ijassa-713 151 29 solving solve VERB ijassa-713 151 30 uncertain uncertain ADJ ijassa-713 151 31 differential differential ADJ ijassa-713 151 32 equations equation NOUN ijassa-713 151 33 . . PUNCT ijassa-713 152 1 step step NOUN ijassa-713 152 2 3 3 NUM ijassa-713 152 3 . . PUNCT ijassa-713 153 1 set set VERB ijassa-713 153 2 𝑖 𝑖 X ijassa-713 153 3 = = PUNCT ijassa-713 153 4 𝑖 𝑖 PROPN ijassa-713 154 1 + + NOUN ijassa-713 154 2 1 1 NUM ijassa-713 154 3 , , PUNCT ijassa-713 154 4 repeat repeat VERB ijassa-713 154 5 step step NOUN ijassa-713 154 6 2 2 NUM ijassa-713 154 7 and and CCONJ ijassa-713 154 8 step step VERB ijassa-713 154 9 3 3 NUM ijassa-713 154 10 for for ADP ijassa-713 154 11 𝑁 𝑁 PROPN ijassa-713 154 12 times time NOUN ijassa-713 154 13 , , PUNCT ijassa-713 154 14 then then ADV ijassa-713 154 15 𝑋(𝑑)𝛼 𝑋(𝑑)𝛼 PROPN ijassa-713 154 16 is be AUX ijassa-713 154 17 derived derive VERB ijassa-713 154 18 . . PUNCT ijassa-713 155 1 go go VERB ijassa-713 155 2 back back ADV ijassa-713 155 3 to to PART ijassa-713 155 4 step step VERB ijassa-713 155 5 1 1 NUM ijassa-713 155 6 until until ADP ijassa-713 155 7 𝑑𝑖 𝑑𝑖 NOUN ijassa-713 155 8 = = SYM ijassa-713 155 9 𝑏 𝑏 NOUN ijassa-713 155 10 , , PUNCT ijassa-713 155 11 table table NOUN ijassa-713 155 12 4.4 4.4 NUM ijassa-713 155 13 : : PUNCT ijassa-713 155 14 results result NOUN ijassa-713 155 15 of of ADP ijassa-713 155 16 analytical analytical ADJ ijassa-713 155 17 solution solution NOUN ijassa-713 155 18 to to ADP ijassa-713 155 19 the the DET ijassa-713 155 20 model model NOUN ijassa-713 155 21 with with ADP ijassa-713 155 22 β„Ž β„Ž X ijassa-713 155 23 = = NOUN ijassa-713 155 24 0.05 0.05 NUM ijassa-713 155 25 , , PUNCT ijassa-713 155 26 π‘Ž π‘Ž PROPN ijassa-713 155 27 ≀ ≀ NUM ijassa-713 155 28 𝑑 𝑑 PROPN ijassa-713 155 29 ≀ ≀ NOUN ijassa-713 155 30 𝑏 𝑏 NOUN ijassa-713 155 31 , , PUNCT ijassa-713 155 32 π‘Ž π‘Ž NOUN ijassa-713 155 33 = = SYM ijassa-713 155 34 0 0 NUM ijassa-713 155 35 , , PUNCT ijassa-713 155 36 𝑏 𝑏 NOUN ijassa-713 155 37 = = SYM ijassa-713 155 38 1 1 NUM ijassa-713 155 39 , , PUNCT ijassa-713 155 40 πœ‚ πœ‚ NOUN ijassa-713 155 41 = = SYM ijassa-713 155 42 0.9 0.9 NUM ijassa-713 155 43 , , PUNCT ijassa-713 155 44 πœ† πœ† NOUN ijassa-713 155 45 = = SYM ijassa-713 155 46 0.1 0.1 NUM ijassa-713 155 47 and and CCONJ ijassa-713 155 48 𝑋0 𝑋0 NOUN ijassa-713 155 49 = = SYM ijassa-713 155 50 18.011 18.011 NUM ijassa-713 155 51 πœ“ πœ“ NOUN ijassa-713 155 52 x x X ijassa-713 155 53 j j NOUN ijassa-713 155 54 -9 -9 PROPN ijassa-713 155 55 -1175.785 -1175.785 PUNCT ijassa-713 156 1 16.657 16.657 NUM ijassa-713 156 2 -7 -7 INTJ ijassa-713 156 3 -28.783 -28.783 PROPN ijassa-713 156 4 11.209 11.209 NUM ijassa-713 156 5 -5 -5 NOUN ijassa-713 156 6 -0.277 -0.277 PROPN ijassa-713 156 7 6.812 6.812 NUM ijassa-713 156 8 -3 -3 PUNCT ijassa-713 156 9 -0.118 -0.118 NUM ijassa-713 156 10 5.941 5.941 NUM ijassa-713 156 11 -1 -1 CCONJ ijassa-713 156 12 -1.612 -1.612 PUNCT ijassa-713 157 1 6.916 6.916 NUM ijassa-713 157 2 1 1 NUM ijassa-713 157 3 19.050 19.050 NUM ijassa-713 157 4 8.854 8.854 NUM ijassa-713 157 5 3 3 NUM ijassa-713 157 6 95.377 95.377 NUM ijassa-713 157 7 11.609 11.609 NUM ijassa-713 157 8 5 5 NUM ijassa-713 157 9 91.492 91.492 NUM ijassa-713 157 10 12.166 12.166 NUM ijassa-713 157 11 7 7 NUM ijassa-713 157 12 77242.383 77242.383 NUM ijassa-713 157 13 24.684 24.684 NUM ijassa-713 157 14 9 9 NUM ijassa-713 157 15 4.159 4.159 NUM ijassa-713 157 16 Γ— Γ— NOUN ijassa-713 157 17 106 106 NUM ijassa-713 157 18 37.710 37.710 NUM ijassa-713 157 19 table table NOUN ijassa-713 157 20 4.5 4.5 NUM ijassa-713 157 21 : : PUNCT ijassa-713 157 22 results result NOUN ijassa-713 157 23 of of ADP ijassa-713 157 24 numerical numerical ADJ ijassa-713 157 25 solution solution NOUN ijassa-713 157 26 to to ADP ijassa-713 157 27 the the DET ijassa-713 157 28 model model NOUN ijassa-713 157 29 ( ( PUNCT ijassa-713 157 30 β„Ž β„Ž X ijassa-713 157 31 = = NOUN ijassa-713 157 32 0.05 0.05 NUM ijassa-713 157 33 , , PUNCT ijassa-713 157 34 π‘Ž π‘Ž NOUN ijassa-713 157 35 = = SYM ijassa-713 157 36 0 0 NUM ijassa-713 157 37 , , PUNCT ijassa-713 157 38 𝑏 𝑏 NOUN ijassa-713 157 39 = = SYM ijassa-713 157 40 1 1 NUM ijassa-713 157 41 , , PUNCT ijassa-713 157 42 πœ‚ πœ‚ NOUN ijassa-713 157 43 = = SYM ijassa-713 157 44 0.9 0.9 NUM ijassa-713 157 45 , , PUNCT ijassa-713 157 46 πœ† πœ† NOUN ijassa-713 157 47 = = SYM ijassa-713 157 48 0.1 0.1 NUM ijassa-713 157 49 and and CCONJ ijassa-713 157 50 𝑋0 𝑋0 NOUN ijassa-713 157 51 = = SYM ijassa-713 157 52 18.011 18.011 NUM ijassa-713 157 53 ) ) PUNCT ijassa-713 157 54 πœ“ πœ“ NOUN ijassa-713 157 55 x x SYM ijassa-713 157 56 j j NOUN ijassa-713 157 57 -9 -9 PROPN ijassa-713 157 58 -1638.001 -1638.001 PUNCT ijassa-713 157 59 17.218 17.218 NUM ijassa-713 157 60 -7 -7 NOUN ijassa-713 157 61 -31.576 -31.576 PROPN ijassa-713 157 62 11.313 11.313 NUM ijassa-713 157 63 t. t. NOUN ijassa-713 157 64 latunde latunde VERB ijassa-713 157 65 61 61 NUM ijassa-713 157 66 copyright copyright NOUN ijassa-713 157 67 Β© Β© PROPN ijassa-713 157 68 2019 2019 NUM ijassa-713 157 69 assa assa NOUN ijassa-713 157 70 . . PUNCT ijassa-713 158 1 adv adv PROPN ijassa-713 158 2 . . PUNCT ijassa-713 159 1 in in ADP ijassa-713 159 2 systems system NOUN ijassa-713 159 3 science science NOUN ijassa-713 159 4 and and CCONJ ijassa-713 159 5 appl appl NOUN ijassa-713 159 6 . . PUNCT ijassa-713 160 1 ( ( PUNCT ijassa-713 160 2 2019 2019 NUM ijassa-713 160 3 ) ) PUNCT ijassa-713 160 4 -5 -5 INTJ ijassa-713 160 5 -0.322 -0.322 PUNCT ijassa-713 161 1 6.916 6.916 NUM ijassa-713 161 2 -3 -3 SYM ijassa-713 161 3 -0.150 -0.150 NUM ijassa-713 161 4 6.088 6.088 NUM ijassa-713 161 5 -1 -1 SYM ijassa-713 161 6 -3.037 -3.037 NUM ijassa-713 162 1 7.368 7.368 NUM ijassa-713 162 2 1 1 NUM ijassa-713 162 3 19.007 19.007 NUM ijassa-713 162 4 8.852 8.852 NUM ijassa-713 162 5 3 3 NUM ijassa-713 162 6 93.596 93.596 NUM ijassa-713 162 7 11.587 11.587 NUM ijassa-713 162 8 5 5 NUM ijassa-713 162 9 84.931 84.931 NUM ijassa-713 162 10 12.076 12.076 NUM ijassa-713 162 11 7 7 NUM ijassa-713 162 12 74991.214 74991.214 NUM ijassa-713 162 13 24.612 24.612 NUM ijassa-713 162 14 9 9 NUM ijassa-713 162 15 3.524 3.524 NUM ijassa-713 162 16 Γ— Γ— NOUN ijassa-713 162 17 106 106 NUM ijassa-713 162 18 37.090 37.090 NUM ijassa-713 162 19 furthermore furthermore ADV ijassa-713 162 20 , , PUNCT ijassa-713 162 21 using use VERB ijassa-713 162 22 the the DET ijassa-713 162 23 available available ADJ ijassa-713 162 24 data datum NOUN ijassa-713 162 25 , , PUNCT ijassa-713 162 26 the the DET ijassa-713 162 27 numerical numerical ADJ ijassa-713 162 28 and and CCONJ ijassa-713 162 29 analytical analytical ADJ ijassa-713 162 30 solution solution NOUN ijassa-713 162 31 to to ADP ijassa-713 162 32 the the DET ijassa-713 162 33 asset asset NOUN ijassa-713 162 34 - - PUNCT ijassa-713 162 35 liability liability NOUN ijassa-713 162 36 management management NOUN ijassa-713 162 37 problem problem NOUN ijassa-713 162 38 was be AUX ijassa-713 162 39 presented present VERB ijassa-713 162 40 . . PUNCT ijassa-713 163 1 using use VERB ijassa-713 163 2 the the DET ijassa-713 163 3 net net ADJ ijassa-713 163 4 worth worth NOUN ijassa-713 163 5 of of ADP ijassa-713 163 6 the the DET ijassa-713 163 7 year year NOUN ijassa-713 163 8 2007 2007 NUM ijassa-713 163 9 to to ADP ijassa-713 163 10 2016 2016 NUM ijassa-713 163 11 were be AUX ijassa-713 163 12 to to PART ijassa-713 163 13 study study VERB ijassa-713 163 14 the the DET ijassa-713 163 15 behaviour behaviour NOUN ijassa-713 163 16 of of ADP ijassa-713 163 17 the the DET ijassa-713 163 18 optimal optimal ADJ ijassa-713 163 19 control control NOUN ijassa-713 163 20 in in ADP ijassa-713 163 21 each each DET ijassa-713 163 22 year year NOUN ijassa-713 163 23 and and CCONJ ijassa-713 163 24 provide provide VERB ijassa-713 163 25 a a DET ijassa-713 163 26 control control NOUN ijassa-713 163 27 policy policy NOUN ijassa-713 163 28 to to ADP ijassa-713 163 29 the the DET ijassa-713 163 30 problem problem NOUN ijassa-713 163 31 . . PUNCT ijassa-713 164 1 let let VERB ijassa-713 164 2 πœ“π‘‚ πœ“π‘‚ CCONJ ijassa-713 164 3 be be AUX ijassa-713 164 4 the the DET ijassa-713 164 5 optimal optimal ADJ ijassa-713 164 6 control control NOUN ijassa-713 164 7 which which PRON ijassa-713 164 8 implies imply VERB ijassa-713 164 9 the the DET ijassa-713 164 10 rate rate NOUN ijassa-713 164 11 of of ADP ijassa-713 164 12 capital capital NOUN ijassa-713 164 13 asset asset NOUN ijassa-713 164 14 such such ADJ ijassa-713 164 15 that that SCONJ ijassa-713 164 16 the the DET ijassa-713 164 17 expected expect VERB ijassa-713 164 18 present present ADJ ijassa-713 164 19 value value NOUN ijassa-713 164 20 of of ADP ijassa-713 164 21 the the DET ijassa-713 164 22 utility utility NOUN ijassa-713 164 23 of of ADP ijassa-713 164 24 assets asset NOUN ijassa-713 164 25 , , PUNCT ijassa-713 164 26 and and CCONJ ijassa-713 164 27 πœ“π΄ πœ“π΄ PROPN ijassa-713 164 28 be be AUX ijassa-713 164 29 the the DET ijassa-713 164 30 actual actual ADJ ijassa-713 164 31 control control NOUN ijassa-713 164 32 which which PRON ijassa-713 164 33 is be AUX ijassa-713 164 34 obtained obtain VERB ijassa-713 164 35 from from ADP ijassa-713 164 36 the the DET ijassa-713 164 37 given give VERB ijassa-713 164 38 ratio ratio NOUN ijassa-713 164 39 of of ADP ijassa-713 164 40 capital capital NOUN ijassa-713 164 41 asset asset NOUN ijassa-713 164 42 and and CCONJ ijassa-713 164 43 net net ADJ ijassa-713 164 44 worth worth NOUN ijassa-713 164 45 . . PUNCT ijassa-713 165 1 the the DET ijassa-713 165 2 optimal optimal ADJ ijassa-713 165 3 control control NOUN ijassa-713 165 4 πœ“π‘‚ πœ“π‘‚ PROPN ijassa-713 165 5 for for ADP ijassa-713 165 6 each each DET ijassa-713 165 7 year year NOUN ijassa-713 165 8 was be AUX ijassa-713 165 9 derived derive VERB ijassa-713 165 10 analytically analytically ADV ijassa-713 165 11 using use VERB ijassa-713 165 12 the the DET ijassa-713 165 13 equation equation NOUN ijassa-713 165 14 of of ADP ijassa-713 165 15 optimality optimality NOUN ijassa-713 165 16 proposed propose VERB ijassa-713 165 17 in in ADP ijassa-713 165 18 [ [ X ijassa-713 165 19 19 19 NUM ijassa-713 165 20 ] ] PUNCT ijassa-713 165 21 for for ADP ijassa-713 165 22 uncertain uncertain ADJ ijassa-713 165 23 optimal optimal ADJ ijassa-713 165 24 control control NOUN ijassa-713 165 25 problem problem NOUN ijassa-713 165 26 , , PUNCT ijassa-713 165 27 where where SCONJ ijassa-713 165 28 πœ“π‘‚ πœ“π‘‚ ADP ijassa-713 165 29 = = SYM ijassa-713 165 30 ( ( PUNCT ijassa-713 165 31 πœ‡+𝑗+𝑔+πœ”βˆ’β„Ž)πœ†βˆ’πœ‚ πœ‡+𝑗+𝑔+πœ”βˆ’β„Ž)πœ†βˆ’πœ‚ PROPN ijassa-713 165 32 ( ( PUNCT ijassa-713 165 33 1βˆ’πœ†)(πœ…+π›½βˆ’πœ” 1βˆ’πœ†)(πœ…+π›½βˆ’πœ” NUM ijassa-713 165 34 ) ) PUNCT ijassa-713 165 35 and and CCONJ ijassa-713 165 36 the the DET ijassa-713 165 37 actual actual ADJ ijassa-713 165 38 control control NOUN ijassa-713 165 39 is be AUX ijassa-713 165 40 πœ“π΄ πœ“π΄ PROPN ijassa-713 165 41 = = SYM ijassa-713 165 42 𝐴(𝑑 𝐴(𝑑 PROPN ijassa-713 165 43 ) ) PUNCT ijassa-713 165 44 𝑋(𝑑 𝑋(𝑑 PROPN ijassa-713 165 45 ) ) PUNCT ijassa-713 165 46 . . PUNCT ijassa-713 166 1 table table NOUN ijassa-713 166 2 4.6 4.6 NUM ijassa-713 166 3 : : PUNCT ijassa-713 166 4 results result NOUN ijassa-713 166 5 on on ADP ijassa-713 166 6 performance performance NOUN ijassa-713 166 7 of of ADP ijassa-713 166 8 capital capital NOUN ijassa-713 166 9 asset asset NOUN ijassa-713 166 10 year year NOUN ijassa-713 166 11 πœ“π΄ πœ“π΄ PROPN ijassa-713 166 12 πœ“π‘‚ πœ“π‘‚ PROPN ijassa-713 166 13 πœ“π΄ πœ“π΄ PROPN ijassa-713 167 1 πœ“π‘‚ πœ“π‘‚ CCONJ ijassa-713 167 2 2007 2007 NUM ijassa-713 167 3 -2.22 -2.22 PRON ijassa-713 167 4 -4.09 -4.09 NUM ijassa-713 167 5 1.87 1.87 NUM ijassa-713 167 6 2008 2008 NUM ijassa-713 167 7 -4.24 -4.24 NOUN ijassa-713 167 8 -5.88 -5.88 NUM ijassa-713 167 9 1.64 1.64 NUM ijassa-713 167 10 2009 2009 NUM ijassa-713 167 11 -3.84 -3.84 NUM ijassa-713 167 12 -5.09 -5.09 NUM ijassa-713 167 13 1.25 1.25 NUM ijassa-713 167 14 2010 2010 NUM ijassa-713 167 15 2.80 2.80 NUM ijassa-713 167 16 0.67 0.67 NUM ijassa-713 167 17 2.13 2.13 NUM ijassa-713 167 18 2011 2011 NUM ijassa-713 167 19 3.98 3.98 NUM ijassa-713 167 20 1.42 1.42 NUM ijassa-713 167 21 2.56 2.56 NUM ijassa-713 167 22 2012 2012 NUM ijassa-713 167 23 3.89 3.89 NUM ijassa-713 167 24 1.22 1.22 NUM ijassa-713 167 25 2.67 2.67 NUM ijassa-713 167 26 2013 2013 NUM ijassa-713 167 27 8.63 8.63 NUM ijassa-713 167 28 5.59 5.59 NUM ijassa-713 167 29 3.04 3.04 NUM ijassa-713 167 30 2014 2014 NUM ijassa-713 167 31 4.76 4.76 NUM ijassa-713 167 32 2.01 2.01 NUM ijassa-713 167 33 2.75 2.75 NUM ijassa-713 167 34 2015 2015 NUM ijassa-713 167 35 12.09 12.09 NUM ijassa-713 167 36 7.88 7.88 NUM ijassa-713 167 37 4.21 4.21 NUM ijassa-713 167 38 2016 2016 NUM ijassa-713 167 39 4.62 4.62 NUM ijassa-713 167 40 0.74 0.74 NUM ijassa-713 167 41 3.88 3.88 NUM ijassa-713 167 42 the the DET ijassa-713 167 43 warning warning NOUN ijassa-713 167 44 signal signal NOUN ijassa-713 167 45 will will AUX ijassa-713 167 46 be be AUX ijassa-713 167 47 based base VERB ijassa-713 167 48 on on ADP ijassa-713 167 49 the the DET ijassa-713 167 50 difference difference NOUN ijassa-713 167 51 between between ADP ijassa-713 167 52 the the DET ijassa-713 167 53 actual actual ADJ ijassa-713 167 54 liability liability NOUN ijassa-713 167 55 ratio ratio NOUN ijassa-713 167 56 𝜏𝐴 𝜏𝐴 PROPN ijassa-713 167 57 and and CCONJ ijassa-713 167 58 the the DET ijassa-713 167 59 optimal optimal ADJ ijassa-713 167 60 liability liability NOUN ijassa-713 167 61 ratio ratio NOUN ijassa-713 167 62 πœπ‘‚. πœπ‘‚. ADJ ijassa-713 167 63 table table NOUN ijassa-713 167 64 4.7 4.7 NUM ijassa-713 167 65 : : PUNCT ijassa-713 167 66 warning warning NOUN ijassa-713 167 67 signal signal NOUN ijassa-713 167 68 year year NOUN ijassa-713 167 69 𝜏𝐴 𝜏𝐴 PROPN ijassa-713 167 70 πœπ‘‚ πœπ‘‚ PROPN ijassa-713 167 71 𝜏𝐴 𝜏𝐴 PROPN ijassa-713 167 72 πœπ‘‚ πœπ‘‚ PROPN ijassa-713 167 73 2007 2007 NUM ijassa-713 167 74 -3.22 -3.22 NUM ijassa-713 167 75 -5.09 -5.09 VERB ijassa-713 167 76 0.87 0.87 NUM ijassa-713 167 77 62 62 NUM ijassa-713 167 78 optimal optimal ADJ ijassa-713 167 79 values value NOUN ijassa-713 167 80 in in ADP ijassa-713 167 81 uncertin uncertin PROPN ijassa-713 167 82 optimal optimal ADJ ijassa-713 167 83 control control NOUN ijassa-713 167 84 model model NOUN ijassa-713 167 85 copyright copyright NOUN ijassa-713 167 86 Β© Β© PROPN ijassa-713 167 87 2019 2019 NUM ijassa-713 167 88 assa assa PROPN ijassa-713 167 89 adv adv PROPN ijassa-713 167 90 . . PUNCT ijassa-713 168 1 in in ADP ijassa-713 168 2 systems system NOUN ijassa-713 168 3 science science NOUN ijassa-713 168 4 and and CCONJ ijassa-713 168 5 appl appl NOUN ijassa-713 168 6 . . PUNCT ijassa-713 169 1 ( ( PUNCT ijassa-713 169 2 2019 2019 NUM ijassa-713 169 3 ) ) PUNCT ijassa-713 169 4 2008 2008 NUM ijassa-713 169 5 -5.24 -5.24 NUM ijassa-713 169 6 -6.88 -6.88 NUM ijassa-713 169 7 0.64 0.64 NUM ijassa-713 169 8 2009 2009 NUM ijassa-713 169 9 -4.84 -4.84 NUM ijassa-713 169 10 -6.09 -6.09 VERB ijassa-713 169 11 0.25 0.25 NUM ijassa-713 169 12 2010 2010 NUM ijassa-713 169 13 1.80 1.80 NUM ijassa-713 169 14 -0.33 -0.33 NOUN ijassa-713 169 15 1.13 1.13 NUM ijassa-713 169 16 2011 2011 NUM ijassa-713 169 17 2.98 2.98 NUM ijassa-713 169 18 0.42 0.42 NUM ijassa-713 169 19 1.56 1.56 NUM ijassa-713 169 20 2012 2012 NUM ijassa-713 169 21 2.89 2.89 NUM ijassa-713 169 22 0.22 0.22 NUM ijassa-713 169 23 2.67 2.67 NUM ijassa-713 169 24 2013 2013 NUM ijassa-713 169 25 7.63 7.63 NUM ijassa-713 169 26 4.59 4.59 NUM ijassa-713 169 27 2.04 2.04 NUM ijassa-713 169 28 2014 2014 NUM ijassa-713 169 29 3.76 3.76 NUM ijassa-713 169 30 1.01 1.01 NUM ijassa-713 169 31 1.75 1.75 NUM ijassa-713 169 32 2015 2015 NUM ijassa-713 169 33 11.09 11.09 NUM ijassa-713 169 34 6.88 6.88 NUM ijassa-713 169 35 3.21 3.21 NUM ijassa-713 169 36 2016 2016 NUM ijassa-713 169 37 3.62 3.62 NUM ijassa-713 169 38 -0.26 -0.26 NOUN ijassa-713 169 39 2.88 2.88 NUM ijassa-713 169 40 4.2 4.2 NUM ijassa-713 169 41 optimal optimal ADJ ijassa-713 169 42 u u NOUN ijassa-713 169 43 , , PUNCT ijassa-713 169 44 𝝀 𝝀 NOUN ijassa-713 169 45 and and CCONJ ijassa-713 169 46 𝜼 𝜼 VERB ijassa-713 169 47 by by ADP ijassa-713 169 48 hyperbolic hyperbolic ADJ ijassa-713 169 49 absolute absolute ADJ ijassa-713 169 50 risk risk NOUN ijassa-713 169 51 aversion aversion NOUN ijassa-713 169 52 utility utility NOUN ijassa-713 169 53 function function NOUN ijassa-713 169 54 , , PUNCT ijassa-713 169 55 π‘ˆ(𝐴 π‘ˆ(𝐴 PROPN ijassa-713 169 56 ) ) PUNCT ijassa-713 169 57 = = PUNCT ijassa-713 170 1 ( ( PUNCT ijassa-713 170 2 1 1 NUM ijassa-713 170 3 πœ† πœ† X ijassa-713 170 4 π΄πœ† π΄πœ† PROPN ijassa-713 170 5 , , PUNCT ijassa-713 170 6 0 0 PUNCT ijassa-713 170 7 < < X ijassa-713 170 8 πœ† πœ† X ijassa-713 170 9 < < X ijassa-713 170 10 1 1 NUM ijassa-713 170 11 lna lna PROPN ijassa-713 170 12 , , PUNCT ijassa-713 170 13 πœ† πœ† PROPN ijassa-713 170 14 = = SYM ijassa-713 170 15 0 0 NUM ijassa-713 170 16 π‘‘π‘ˆ π‘‘π‘ˆ VERB ijassa-713 170 17 π‘‘πœ† π‘‘πœ† NOUN ijassa-713 170 18 = = SYM ijassa-713 170 19 0 0 NUM ijassa-713 170 20 βˆ’ βˆ’ PROPN ijassa-713 170 21 1 1 NUM ijassa-713 170 22 πœ†2 πœ†2 NOUN ijassa-713 170 23 π΄πœ† π΄πœ† PROPN ijassa-713 170 24 + + PROPN ijassa-713 170 25 1 1 NUM ijassa-713 170 26 πœ† πœ† PRON ijassa-713 170 27 π΄πœ†ln𝐴 π΄πœ†ln𝐴 PROPN ijassa-713 170 28 = = SYM ijassa-713 170 29 0 0 NUM ijassa-713 170 30 1 1 NUM ijassa-713 170 31 πœ† πœ† NOUN ijassa-713 170 32 = = PUNCT ijassa-713 170 33 ln𝐴 ln𝐴 NOUN ijassa-713 170 34 πœ† πœ† NOUN ijassa-713 171 1 = = SYM ijassa-713 171 2 1 1 NUM ijassa-713 171 3 ln𝐴 ln𝐴 NOUN ijassa-713 171 4 hence hence ADV ijassa-713 171 5 , , PUNCT ijassa-713 171 6 the the DET ijassa-713 171 7 optimal optimal ADJ ijassa-713 171 8 πœ† πœ† NOUN ijassa-713 171 9 is be AUX ijassa-713 171 10 πœ†βˆ— πœ†βˆ— NOUN ijassa-713 171 11 = = SYM ijassa-713 171 12 1 1 NUM ijassa-713 171 13 ln𝐴 ln𝐴 NOUN ijassa-713 171 14 . . PUNCT ijassa-713 172 1 similarly similarly ADV ijassa-713 172 2 , , PUNCT ijassa-713 172 3 optimal optimal ADJ ijassa-713 172 4 π‘ˆ π‘ˆ PROPN ijassa-713 172 5 is be AUX ijassa-713 172 6 π‘ˆβˆ— π‘ˆβˆ— NOUN ijassa-713 172 7 where where SCONJ ijassa-713 172 8 π‘ˆβˆ— π‘ˆβˆ— PROPN ijassa-713 172 9 = = NOUN ijassa-713 172 10 1 1 NUM ijassa-713 172 11 πœ†βˆ— πœ†βˆ— NOUN ijassa-713 172 12 π΄πœ†βˆ— π΄πœ†βˆ— NOUN ijassa-713 172 13 = = NOUN ijassa-713 172 14 ( ( PUNCT ijassa-713 172 15 ln𝐴)𝐴 ln𝐴)𝐴 NOUN ijassa-713 172 16 1 1 NUM ijassa-713 172 17 ln𝐴 ln𝐴 NOUN ijassa-713 172 18 from from ADP ijassa-713 172 19 table table NOUN ijassa-713 172 20 4.2 4.2 NUM ijassa-713 172 21 , , PUNCT ijassa-713 172 22 let let VERB ijassa-713 172 23 𝐴1 𝐴1 PROPN ijassa-713 172 24 = = SYM ijassa-713 172 25 15.396 15.396 NUM ijassa-713 172 26 and and CCONJ ijassa-713 172 27 𝐴2 𝐴2 PROPN ijassa-713 172 28 = = PUNCT ijassa-713 172 29 85.737 85.737 NUM ijassa-713 172 30 where where SCONJ ijassa-713 172 31 πœ† πœ† ADP ijassa-713 172 32 = = X ijassa-713 172 33 πœ†1 πœ†1 PROPN ijassa-713 172 34 and and CCONJ ijassa-713 172 35 𝐴 𝐴 PROPN ijassa-713 172 36 = = SYM ijassa-713 172 37 𝐴1 𝐴1 PROPN ijassa-713 172 38 . . PUNCT ijassa-713 173 1 this this PRON ijassa-713 173 2 implies imply VERB ijassa-713 173 3 πœ†1 πœ†1 NOUN ijassa-713 173 4 = = SYM ijassa-713 173 5 1 1 NUM ijassa-713 173 6 ln𝐴1 ln𝐴1 NOUN ijassa-713 173 7 = = NOUN ijassa-713 173 8 0.366 0.366 NUM ijassa-713 173 9 let let VERB ijassa-713 173 10 π‘ˆ π‘ˆ PROPN ijassa-713 173 11 = = SYM ijassa-713 173 12 π‘ˆ1 π‘ˆ1 NOUN ijassa-713 173 13 π‘ˆ1 π‘ˆ1 NOUN ijassa-713 173 14 = = SYM ijassa-713 173 15 ( ( PUNCT ijassa-713 173 16 ln𝐴1)𝐴1 ln𝐴1)𝐴1 NOUN ijassa-713 173 17 1 1 NUM ijassa-713 173 18 ln𝐴1 ln𝐴1 NOUN ijassa-713 173 19 = = NOUN ijassa-713 173 20 7.432 7.432 NUM ijassa-713 173 21 and and CCONJ ijassa-713 173 22 let let VERB ijassa-713 173 23 πœ† πœ† NOUN ijassa-713 173 24 = = SYM ijassa-713 173 25 πœ†2 πœ†2 PROPN ijassa-713 173 26 , , PUNCT ijassa-713 173 27 𝐴 𝐴 PROPN ijassa-713 173 28 = = PUNCT ijassa-713 173 29 𝐴2 𝐴2 PROPN ijassa-713 173 30 πœ†2 πœ†2 NOUN ijassa-713 173 31 = = NOUN ijassa-713 173 32 1 1 NUM ijassa-713 173 33 ln𝐴2 ln𝐴2 NUM ijassa-713 173 34 = = PUNCT ijassa-713 173 35 0.225 0.225 NUM ijassa-713 173 36 π‘ˆ2 π‘ˆ2 NOUN ijassa-713 174 1 = = PUNCT ijassa-713 175 1 ( ( PUNCT ijassa-713 175 2 ln𝐴2)𝐴1 ln𝐴2)𝐴1 NOUN ijassa-713 175 3 1 1 NUM ijassa-713 175 4 ln𝐴2 ln𝐴2 NUM ijassa-713 175 5 = = SYM ijassa-713 175 6 12.100 12.100 NUM ijassa-713 175 7 therefore therefore ADV ijassa-713 175 8 , , PUNCT ijassa-713 175 9 πœ†2 πœ†2 PROPN ijassa-713 175 10 ≑ ≑ PROPN ijassa-713 175 11 πœ†βˆ— πœ†βˆ— NOUN ijassa-713 175 12 = = PUNCT ijassa-713 175 13 0.225 0.225 NUM ijassa-713 175 14 and and CCONJ ijassa-713 175 15 π‘ˆ2 π‘ˆ2 PROPN ijassa-713 175 16 ≑ ≑ PROPN ijassa-713 175 17 π‘ˆβˆ— π‘ˆβˆ— PROPN ijassa-713 176 1 = = PUNCT ijassa-713 176 2 12.100 12.100 NUM ijassa-713 176 3 also also ADV ijassa-713 176 4 , , PUNCT ijassa-713 176 5 from from ADP ijassa-713 176 6 equation equation NOUN ijassa-713 176 7 ( ( PUNCT ijassa-713 176 8 3.1 3.1 NUM ijassa-713 176 9 ) ) PUNCT ijassa-713 176 10 t. t. NOUN ijassa-713 176 11 latunde latunde VERB ijassa-713 176 12 63 63 NUM ijassa-713 176 13 copyright copyright NOUN ijassa-713 176 14 Β© Β© PROPN ijassa-713 176 15 2019 2019 NUM ijassa-713 176 16 assa assa NOUN ijassa-713 176 17 . . PUNCT ijassa-713 177 1 adv adv PROPN ijassa-713 177 2 . . PUNCT ijassa-713 178 1 in in ADP ijassa-713 178 2 systems system NOUN ijassa-713 178 3 science science NOUN ijassa-713 178 4 and and CCONJ ijassa-713 178 5 appl appl NOUN ijassa-713 178 6 . . PUNCT ijassa-713 179 1 ( ( PUNCT ijassa-713 179 2 2019 2019 NUM ijassa-713 179 3 ) ) PUNCT ijassa-713 179 4 𝐽 𝐽 NOUN ijassa-713 179 5 = = NOUN ijassa-713 179 6 max𝐸𝐢 max𝐸𝐢 NOUN ijassa-713 179 7 [ [ PUNCT ijassa-713 179 8 ∫ ∫ PROPN ijassa-713 179 9 𝑑𝑓 𝑑𝑓 NOUN ijassa-713 179 10 𝑑0 𝑑0 PROPN ijassa-713 179 11 π‘’βˆ’πœ‚π‘‘π‘ˆ(𝐴(𝑑))𝑑𝑑 π‘’βˆ’πœ‚π‘‘π‘ˆ(𝐴(𝑑))𝑑𝑑 PROPN ijassa-713 179 12 ] ] X ijassa-713 179 13 = = SYM ijassa-713 179 14 maxπ‘ˆ(𝐴)max maxπ‘ˆ(𝐴)max X ijassa-713 179 15 ∫ ∫ PROPN ijassa-713 180 1 1 1 NUM ijassa-713 180 2 0 0 NUM ijassa-713 180 3 π‘’βˆ’πœ‚π‘‘π‘‘π‘‘ π‘’βˆ’πœ‚π‘‘π‘‘π‘‘ NOUN ijassa-713 180 4 = = PUNCT ijassa-713 180 5 π‘ˆβˆ—max π‘ˆβˆ—max ADJ ijassa-713 180 6 1 1 NUM ijassa-713 180 7 πœ‚ πœ‚ NOUN ijassa-713 180 8 ( ( PUNCT ijassa-713 180 9 1 1 NUM ijassa-713 180 10 βˆ’ βˆ’ NOUN ijassa-713 180 11 π‘’βˆ’πœ‚ π‘’βˆ’πœ‚ ADJ ijassa-713 180 12 ) ) PUNCT ijassa-713 180 13 = = SYM ijassa-713 180 14 1 1 NUM ijassa-713 180 15 πœ‚ πœ‚ NOUN ijassa-713 180 16 π‘ˆβˆ— π‘ˆβˆ— NOUN ijassa-713 180 17 given give VERB ijassa-713 180 18 in in ADP ijassa-713 180 19 table table NOUN ijassa-713 180 20 4.1 4.1 NUM ijassa-713 180 21 is be AUX ijassa-713 180 22 the the DET ijassa-713 180 23 net net ADJ ijassa-713 180 24 present present ADJ ijassa-713 180 25 value value NOUN ijassa-713 180 26 𝐽 𝐽 PROPN ijassa-713 180 27 as as ADP ijassa-713 180 28 𝐴 𝐴 PROPN ijassa-713 180 29 πœ‚+1 πœ‚+1 PROPN ijassa-713 180 30 this this PRON ijassa-713 180 31 implies imply VERB ijassa-713 180 32 𝐴2 𝐴2 PROPN ijassa-713 180 33 πœ‚ πœ‚ PROPN ijassa-713 180 34 + + PROPN ijassa-713 180 35 1 1 NUM ijassa-713 180 36 = = SYM ijassa-713 180 37 π‘ˆβˆ— π‘ˆβˆ— NOUN ijassa-713 180 38 πœ‚ πœ‚ NOUN ijassa-713 180 39 thus thus ADV ijassa-713 180 40 , , PUNCT ijassa-713 180 41 πœ‚βˆ— πœ‚βˆ— PROPN ijassa-713 180 42 = = NOUN ijassa-713 181 1 π‘ˆβˆ— π‘ˆβˆ— PROPN ijassa-713 181 2 𝐴2 𝐴2 PROPN ijassa-713 181 3 βˆ’ βˆ’ PROPN ijassa-713 181 4 π‘ˆβˆ— π‘ˆβˆ— PROPN ijassa-713 181 5 β‡’ β‡’ NOUN ijassa-713 181 6 πœ‚βˆ— πœ‚βˆ— PROPN ijassa-713 182 1 = = NOUN ijassa-713 182 2 0.164 0.164 NUM ijassa-713 182 3 therefore therefore ADV ijassa-713 182 4 , , PUNCT ijassa-713 182 5 using use VERB ijassa-713 182 6 the the DET ijassa-713 182 7 calculated calculated ADJ ijassa-713 182 8 optimal optimal ADJ ijassa-713 182 9 values value NOUN ijassa-713 182 10 , , PUNCT ijassa-713 182 11 the the DET ijassa-713 182 12 following follow VERB ijassa-713 182 13 results result NOUN ijassa-713 182 14 are be AUX ijassa-713 182 15 obtained obtain VERB ijassa-713 182 16 . . PUNCT ijassa-713 183 1 table table NOUN ijassa-713 183 2 4.8 4.8 NUM ijassa-713 183 3 : : PUNCT ijassa-713 183 4 numerical numerical ADJ ijassa-713 183 5 result result NOUN ijassa-713 183 6 of of ADP ijassa-713 183 7 expected expect VERB ijassa-713 183 8 present present ADJ ijassa-713 183 9 value value NOUN ijassa-713 183 10 of of ADP ijassa-713 183 11 utility utility NOUN ijassa-713 183 12 of of ADP ijassa-713 183 13 asset asset NOUN ijassa-713 183 14 𝐽(πœ“)𝛼 𝐽(πœ“)𝛼 PROPN ijassa-713 183 15 with with ADP ijassa-713 183 16 different different ADJ ijassa-713 183 17 𝛼-paths 𝛼-path NOUN ijassa-713 183 18 𝛼 𝛼 ADP ijassa-713 183 19 𝐽(πœ“)𝛼 𝐽(πœ“)𝛼 VERB ijassa-713 183 20 10βˆ’6 10βˆ’6 NUM ijassa-713 183 21 1.152 1.152 NUM ijassa-713 183 22 Γ— Γ— NOUN ijassa-713 183 23 106 106 NUM ijassa-713 183 24 .1 .1 NUM ijassa-713 184 1 25619.235 25619.235 NUM ijassa-713 184 2 .24 .24 NUM ijassa-713 184 3 6056.883 6056.883 NUM ijassa-713 184 4 .38 .38 NUM ijassa-713 184 5 448.529 448.529 NUM ijassa-713 184 6 .52 .52 NUM ijassa-713 184 7 429.982 429.982 NUM ijassa-713 184 8 .64 .64 NUM ijassa-713 184 9 3372.794 3372.794 NUM ijassa-713 184 10 .8 .8 NOUN ijassa-713 184 11 15826.851 15826.851 NUM ijassa-713 184 12 .999999 .999999 NOUN ijassa-713 184 13 1.273 1.273 NUM ijassa-713 184 14 Γ— Γ— NOUN ijassa-713 184 15 106 106 NUM ijassa-713 184 16 5 5 NUM ijassa-713 184 17 . . PUNCT ijassa-713 184 18 conclusion conclusion NOUN ijassa-713 184 19 based base VERB ijassa-713 184 20 on on ADP ijassa-713 184 21 uncertainty uncertainty NOUN ijassa-713 184 22 theory theory NOUN ijassa-713 184 23 , , PUNCT ijassa-713 184 24 an an DET ijassa-713 184 25 optimal optimal ADJ ijassa-713 184 26 control control NOUN ijassa-713 184 27 model model NOUN ijassa-713 184 28 of of ADP ijassa-713 184 29 capital capital NOUN ijassa-713 184 30 asset asset NOUN ijassa-713 184 31 was be AUX ijassa-713 184 32 formulated formulate VERB ijassa-713 184 33 by by ADP ijassa-713 184 34 adapting adapt VERB ijassa-713 184 35 the the DET ijassa-713 184 36 expected expect VERB ijassa-713 184 37 value value NOUN ijassa-713 184 38 operator operator NOUN ijassa-713 184 39 to to PART ijassa-713 184 40 quantify quantify VERB ijassa-713 184 41 the the DET ijassa-713 184 42 objective objective ADJ ijassa-713 184 43 rewards reward NOUN ijassa-713 184 44 in in ADP ijassa-713 184 45 the the DET ijassa-713 184 46 model model NOUN ijassa-713 184 47 . . PUNCT ijassa-713 185 1 furthermore furthermore ADV ijassa-713 185 2 , , PUNCT ijassa-713 185 3 the the DET ijassa-713 185 4 model model NOUN ijassa-713 185 5 was be AUX ijassa-713 185 6 solved solve VERB ijassa-713 185 7 by by ADP ijassa-713 185 8 using use VERB ijassa-713 185 9 some some DET ijassa-713 185 10 optimality optimality NOUN ijassa-713 185 11 criteria criterion NOUN ijassa-713 185 12 to to PART ijassa-713 185 13 derive derive VERB ijassa-713 185 14 the the DET ijassa-713 185 15 optimal optimal ADJ ijassa-713 185 16 values value NOUN ijassa-713 185 17 of of ADP ijassa-713 185 18 some some DET ijassa-713 185 19 input input NOUN ijassa-713 185 20 factors factor NOUN ijassa-713 185 21 , , PUNCT ijassa-713 185 22 thus thus ADV ijassa-713 185 23 applied apply VERB ijassa-713 185 24 to to ADP ijassa-713 185 25 a a DET ijassa-713 185 26 real real ADJ ijassa-713 185 27 life life NOUN ijassa-713 185 28 problem problem NOUN ijassa-713 185 29 . . PUNCT ijassa-713 186 1 in in ADP ijassa-713 186 2 future future ADJ ijassa-713 186 3 work work NOUN ijassa-713 186 4 , , PUNCT ijassa-713 186 5 the the DET ijassa-713 186 6 objective objective NOUN ijassa-713 186 7 of of ADP ijassa-713 186 8 the the DET ijassa-713 186 9 model model NOUN ijassa-713 186 10 may may AUX ijassa-713 186 11 be be AUX ijassa-713 186 12 viewed view VERB ijassa-713 186 13 from from ADP ijassa-713 186 14 the the DET ijassa-713 186 15 perspective perspective NOUN ijassa-713 186 16 of of ADP ijassa-713 186 17 stakeholders stakeholder NOUN ijassa-713 186 18 or or CCONJ ijassa-713 186 19 regulators regulator NOUN ijassa-713 186 20 other other ADJ ijassa-713 186 21 than than ADP ijassa-713 186 22 that that PRON ijassa-713 186 23 of of ADP ijassa-713 186 24 the the DET ijassa-713 186 25 investors investor NOUN ijassa-713 186 26 . . PUNCT ijassa-713 187 1 references reference NOUN ijassa-713 187 2 [ [ X ijassa-713 187 3 1 1 NUM ijassa-713 187 4 ] ] X ijassa-713 187 5 black black NOUN ijassa-713 187 6 , , PUNCT ijassa-713 187 7 f. f. PROPN ijassa-713 187 8 , , PUNCT ijassa-713 187 9 jensen jensen PROPN ijassa-713 187 10 , , PUNCT ijassa-713 187 11 m. m. PROPN ijassa-713 187 12 c. c. PROPN ijassa-713 187 13 & & CCONJ ijassa-713 187 14 scholes scholes PROPN ijassa-713 187 15 , , PUNCT ijassa-713 187 16 m. m. NOUN ijassa-713 187 17 ( ( PUNCT ijassa-713 187 18 1972 1972 NUM ijassa-713 187 19 ) ) PUNCT ijassa-713 187 20 . . PUNCT ijassa-713 188 1 the the DET ijassa-713 188 2 capital capital NOUN ijassa-713 188 3 asset asset NOUN ijassa-713 188 4 pricing pricing NOUN ijassa-713 188 5 model model NOUN ijassa-713 188 6 : : PUNCT ijassa-713 188 7 some some DET ijassa-713 188 8 empirical empirical ADJ ijassa-713 188 9 tests test NOUN ijassa-713 188 10 . . PUNCT ijassa-713 189 1 in in ADP ijassa-713 189 2 m. m. PROPN ijassa-713 189 3 jensen jensen PROPN ijassa-713 189 4 ( ( PUNCT ijassa-713 189 5 ed ed NOUN ijassa-713 189 6 . . PUNCT ijassa-713 189 7 ) ) PUNCT ijassa-713 189 8 , , PUNCT ijassa-713 189 9 studies study NOUN ijassa-713 189 10 in in ADP ijassa-713 189 11 the the DET ijassa-713 189 12 theory theory NOUN ijassa-713 189 13 of of ADP ijassa-713 189 14 capital capital NOUN ijassa-713 189 15 markets market NOUN ijassa-713 189 16 ( ( PUNCT ijassa-713 189 17 pp pp ADJ ijassa-713 189 18 . . PUNCT ijassa-713 189 19 79121 79121 NUM ijassa-713 189 20 ) ) PUNCT ijassa-713 189 21 . . PUNCT ijassa-713 190 1 newyork newyork NOUN ijassa-713 190 2 : : PUNCT ijassa-713 190 3 praeger praeger NOUN ijassa-713 190 4 publishers publisher NOUN ijassa-713 190 5 . . PUNCT ijassa-713 191 1 [ [ X ijassa-713 191 2 2 2 NUM ijassa-713 191 3 ] ] SYM ijassa-713 191 4 deng deng PROPN ijassa-713 191 5 , , PUNCT ijassa-713 191 6 l. l. PROPN ijassa-713 191 7 & & CCONJ ijassa-713 191 8 zhu zhu PROPN ijassa-713 191 9 , , PUNCT ijassa-713 191 10 y. y. PROPN ijassa-713 191 11 ( ( PUNCT ijassa-713 191 12 2012 2012 NUM ijassa-713 191 13 ) ) PUNCT ijassa-713 191 14 . . PUNCT ijassa-713 192 1 an an DET ijassa-713 192 2 uncertain uncertain ADJ ijassa-713 192 3 optimal optimal ADJ ijassa-713 192 4 control control NOUN ijassa-713 192 5 model model NOUN ijassa-713 192 6 with with ADP ijassa-713 192 7 n n PRON ijassa-713 192 8 jumps jump VERB ijassa-713 192 9 and and CCONJ ijassa-713 192 10 application application NOUN ijassa-713 192 11 . . PUNCT ijassa-713 193 1 comsis comsis NOUN ijassa-713 193 2 9(4 9(4 PROPN ijassa-713 193 3 ) ) PUNCT ijassa-713 193 4 , , PUNCT ijassa-713 193 5 1453 1453 NUM ijassa-713 193 6 - - SYM ijassa-713 193 7 1468 1468 NUM ijassa-713 193 8 . . PUNCT ijassa-713 194 1 [ [ X ijassa-713 194 2 3 3 X ijassa-713 194 3 ] ] X ijassa-713 194 4 douglas douglas PROPN ijassa-713 194 5 , , PUNCT ijassa-713 194 6 g. g. PROPN ijassa-713 194 7 w. w. PROPN ijassa-713 194 8 ( ( PUNCT ijassa-713 194 9 1968 1968 NUM ijassa-713 194 10 ) ) PUNCT ijassa-713 194 11 . . PUNCT ijassa-713 195 1 risk risk NOUN ijassa-713 195 2 in in ADP ijassa-713 195 3 the the DET ijassa-713 195 4 equity equity NOUN ijassa-713 195 5 markets market NOUN ijassa-713 195 6 : : PUNCT ijassa-713 195 7 an an DET ijassa-713 195 8 empirical empirical ADJ ijassa-713 195 9 appraisal appraisal NOUN ijassa-713 195 10 of of ADP ijassa-713 195 11 market market NOUN ijassa-713 195 12 efficiency efficiency NOUN ijassa-713 195 13 . . PUNCT ijassa-713 196 1 university university NOUN ijassa-713 196 2 microfilms microfilm NOUN ijassa-713 196 3 , , PUNCT ijassa-713 196 4 inc inc PROPN ijassa-713 196 5 . . PROPN ijassa-713 196 6 , , PUNCT ijassa-713 196 7 ann ann PROPN ijassa-713 196 8 arbor arbor PROPN ijassa-713 196 9 , , PUNCT ijassa-713 196 10 michigan michigan PROPN ijassa-713 196 11 . . PUNCT ijassa-713 197 1 64 64 NUM ijassa-713 197 2 optimal optimal ADJ ijassa-713 197 3 values value NOUN ijassa-713 197 4 in in ADP ijassa-713 197 5 uncertin uncertin PROPN ijassa-713 197 6 optimal optimal ADJ ijassa-713 197 7 control control NOUN ijassa-713 197 8 model model NOUN ijassa-713 197 9 copyright copyright NOUN ijassa-713 197 10 Β© Β© PROPN ijassa-713 197 11 2019 2019 NUM ijassa-713 197 12 assa assa PROPN ijassa-713 197 13 adv adv PROPN ijassa-713 197 14 . . PUNCT ijassa-713 198 1 in in ADP ijassa-713 198 2 systems system NOUN ijassa-713 198 3 science science NOUN ijassa-713 198 4 and and CCONJ ijassa-713 198 5 appl appl NOUN ijassa-713 198 6 . . PUNCT ijassa-713 199 1 ( ( PUNCT ijassa-713 199 2 2019 2019 NUM ijassa-713 199 3 ) ) PUNCT ijassa-713 200 1 [ [ X ijassa-713 200 2 4 4 NUM ijassa-713 200 3 ] ] PUNCT ijassa-713 200 4 fama fama PROPN ijassa-713 200 5 , , PUNCT ijassa-713 200 6 e. e. PROPN ijassa-713 200 7 f. f. PROPN ijassa-713 200 8 & & CCONJ ijassa-713 200 9 macbeth macbeth PROPN ijassa-713 200 10 , , PUNCT ijassa-713 200 11 j. j. PROPN ijassa-713 200 12 d. d. PROPN ijassa-713 200 13 ( ( PUNCT ijassa-713 200 14 1973 1973 NUM ijassa-713 200 15 ) ) PUNCT ijassa-713 200 16 . . PUNCT ijassa-713 201 1 risk risk NOUN ijassa-713 201 2 , , PUNCT ijassa-713 201 3 return return NOUN ijassa-713 201 4 , , PUNCT ijassa-713 201 5 and and CCONJ ijassa-713 201 6 equilibrium equilibrium NOUN ijassa-713 201 7 : : PUNCT ijassa-713 201 8 empirical empirical ADJ ijassa-713 201 9 tests test NOUN ijassa-713 201 10 . . PUNCT ijassa-713 202 1 journal journal NOUN ijassa-713 202 2 of of ADP ijassa-713 202 3 political political ADJ ijassa-713 202 4 economy economy NOUN ijassa-713 202 5 , , PUNCT ijassa-713 202 6 71 71 NUM ijassa-713 202 7 , , PUNCT ijassa-713 202 8 607 607 NUM ijassa-713 202 9 - - SYM ijassa-713 202 10 636 636 NUM ijassa-713 202 11 . . PUNCT ijassa-713 203 1 [ [ X ijassa-713 203 2 5 5 NUM ijassa-713 203 3 ] ] X ijassa-713 203 4 friend friend NOUN ijassa-713 203 5 , , PUNCT ijassa-713 203 6 i. i. PROPN ijassa-713 203 7 & & CCONJ ijassa-713 203 8 blume blume PROPN ijassa-713 203 9 , , PUNCT ijassa-713 203 10 m. m. NOUN ijassa-713 203 11 ( ( PUNCT ijassa-713 203 12 1970 1970 NUM ijassa-713 203 13 ) ) PUNCT ijassa-713 203 14 . . PUNCT ijassa-713 204 1 measurement measurement NOUN ijassa-713 204 2 of of ADP ijassa-713 204 3 portfolio portfolio NOUN ijassa-713 204 4 performance performance NOUN ijassa-713 204 5 under under ADP ijassa-713 204 6 uncertainty uncertainty NOUN ijassa-713 204 7 . . PUNCT ijassa-713 205 1 american american PROPN ijassa-713 205 2 economic economic PROPN ijassa-713 205 3 review review PROPN ijassa-713 205 4 , , PUNCT ijassa-713 205 5 60(4 60(4 NUM ijassa-713 205 6 ) ) PUNCT ijassa-713 205 7 , , PUNCT ijassa-713 205 8 607 607 NUM ijassa-713 205 9 - - SYM ijassa-713 205 10 636 636 NUM ijassa-713 205 11 . . PUNCT ijassa-713 206 1 [ [ X ijassa-713 206 2 6 6 NUM ijassa-713 206 3 ] ] PUNCT ijassa-713 206 4 latunde latunde NOUN ijassa-713 206 5 t. t. PROPN ijassa-713 206 6 & & CCONJ ijassa-713 206 7 bamigbola bamigbola PROPN ijassa-713 206 8 o. o. PROPN ijassa-713 206 9 m. m. PROPN ijassa-713 206 10 ( ( PUNCT ijassa-713 206 11 2016 2016 NUM ijassa-713 206 12 ) ) PUNCT ijassa-713 206 13 . . PUNCT ijassa-713 207 1 uncertain uncertain ADJ ijassa-713 207 2 optimal optimal ADJ ijassa-713 207 3 control control NOUN ijassa-713 207 4 model model NOUN ijassa-713 207 5 for for ADP ijassa-713 207 6 management management NOUN ijassa-713 207 7 of of ADP ijassa-713 207 8 net net ADJ ijassa-713 207 9 risky risky ADJ ijassa-713 207 10 capital capital NOUN ijassa-713 207 11 asset asset NOUN ijassa-713 207 12 . . PUNCT ijassa-713 208 1 iosr iosr ADJ ijassa-713 208 2 journal journal PROPN ijassa-713 208 3 of of ADP ijassa-713 208 4 mathematics mathematics PROPN ijassa-713 208 5 ( ( PUNCT ijassa-713 208 6 iosr iosr PROPN ijassa-713 208 7 - - PUNCT ijassa-713 208 8 jm jm NOUN ijassa-713 208 9 ) ) PUNCT ijassa-713 208 10 , , PUNCT ijassa-713 208 11 12(3 12(3 NUM ijassa-713 208 12 ) ) PUNCT ijassa-713 208 13 , , PUNCT ijassa-713 208 14 2230 2230 NUM ijassa-713 208 15 . . PUNCT ijassa-713 209 1 [ [ X ijassa-713 209 2 7 7 NUM ijassa-713 209 3 ] ] PUNCT ijassa-713 209 4 latunde latunde NOUN ijassa-713 209 5 , , PUNCT ijassa-713 209 6 t. t. PROPN ijassa-713 209 7 & & CCONJ ijassa-713 209 8 bamigbola bamigbola PROPN ijassa-713 209 9 , , PUNCT ijassa-713 209 10 o. o. PROPN ijassa-713 209 11 m. m. NOUN ijassa-713 209 12 ( ( PUNCT ijassa-713 209 13 2018 2018 NUM ijassa-713 209 14 ) ) PUNCT ijassa-713 209 15 . . PUNCT ijassa-713 210 1 parameter parameter PROPN ijassa-713 210 2 estimation estimation NOUN ijassa-713 210 3 and and CCONJ ijassa-713 210 4 sensitivity sensitivity NOUN ijassa-713 210 5 analysis analysis NOUN ijassa-713 210 6 of of ADP ijassa-713 210 7 an an DET ijassa-713 210 8 optimal optimal ADJ ijassa-713 210 9 control control NOUN ijassa-713 210 10 model model NOUN ijassa-713 210 11 for for ADP ijassa-713 210 12 capital capital NOUN ijassa-713 210 13 asset asset NOUN ijassa-713 210 14 management management NOUN ijassa-713 210 15 . . PUNCT ijassa-713 211 1 advances advance NOUN ijassa-713 211 2 in in ADP ijassa-713 211 3 fuzzy fuzzy ADJ ijassa-713 211 4 systems system NOUN ijassa-713 211 5 , , PUNCT ijassa-713 211 6 2018 2018 NUM ijassa-713 211 7 , , PUNCT ijassa-713 211 8 1 1 NUM ijassa-713 211 9 - - SYM ijassa-713 211 10 11 11 NUM ijassa-713 211 11 . . PUNCT ijassa-713 212 1 https//doi.org/10.1155/2018/4756520 https//doi.org/10.1155/2018/4756520 X ijassa-713 213 1 [ [ X ijassa-713 213 2 8 8 NUM ijassa-713 213 3 ] ] X ijassa-713 213 4 liu liu PROPN ijassa-713 213 5 , , PUNCT ijassa-713 213 6 b. b. PROPN ijassa-713 213 7 ( ( PUNCT ijassa-713 213 8 2007 2007 NUM ijassa-713 213 9 ) ) PUNCT ijassa-713 213 10 . . PUNCT ijassa-713 214 1 uncertainty uncertainty NOUN ijassa-713 214 2 theory theory NOUN ijassa-713 214 3 ( ( PUNCT ijassa-713 214 4 2nd 2nd ADJ ijassa-713 214 5 ed ed NOUN ijassa-713 214 6 . . PUNCT ijassa-713 214 7 ) ) PUNCT ijassa-713 214 8 . . PUNCT ijassa-713 215 1 berlin berlin ADJ ijassa-713 215 2 : : PUNCT ijassa-713 215 3 springer springer NOUN ijassa-713 215 4 . . PUNCT ijassa-713 216 1 [ [ X ijassa-713 216 2 9 9 NUM ijassa-713 216 3 ] ] X ijassa-713 216 4 liu liu PROPN ijassa-713 216 5 , , PUNCT ijassa-713 216 6 b. b. PROPN ijassa-713 216 7 ( ( PUNCT ijassa-713 216 8 2008 2008 NUM ijassa-713 216 9 ) ) PUNCT ijassa-713 216 10 . . PUNCT ijassa-713 217 1 fuzzy fuzzy ADJ ijassa-713 217 2 process process NOUN ijassa-713 217 3 , , PUNCT ijassa-713 217 4 hybrid hybrid NOUN ijassa-713 217 5 process process NOUN ijassa-713 217 6 and and CCONJ ijassa-713 217 7 uncertain uncertain ADJ ijassa-713 217 8 process process NOUN ijassa-713 217 9 , , PUNCT ijassa-713 217 10 journal journal NOUN ijassa-713 217 11 of of ADP ijassa-713 217 12 uncertain uncertain ADJ ijassa-713 217 13 systems system NOUN ijassa-713 217 14 , , PUNCT ijassa-713 217 15 2(1 2(1 NUM ijassa-713 217 16 ) ) PUNCT ijassa-713 217 17 , , PUNCT ijassa-713 217 18 3 3 NUM ijassa-713 217 19 - - SYM ijassa-713 217 20 16 16 NUM ijassa-713 217 21 . . PUNCT ijassa-713 218 1 [ [ X ijassa-713 218 2 10 10 NUM ijassa-713 218 3 ] ] X ijassa-713 218 4 liu liu PROPN ijassa-713 218 5 , , PUNCT ijassa-713 218 6 b. b. PROPN ijassa-713 218 7 ( ( PUNCT ijassa-713 218 8 2009 2009 NUM ijassa-713 218 9 ) ) PUNCT ijassa-713 218 10 . . PUNCT ijassa-713 219 1 theory theory NOUN ijassa-713 219 2 and and CCONJ ijassa-713 219 3 practice practice NOUN ijassa-713 219 4 of of ADP ijassa-713 219 5 uncertain uncertain ADJ ijassa-713 219 6 programming programming NOUN ijassa-713 219 7 ( ( PUNCT ijassa-713 219 8 2nd 2nd ADJ ijassa-713 219 9 ed ed NOUN ijassa-713 219 10 . . PUNCT ijassa-713 219 11 ) ) PUNCT ijassa-713 219 12 . . PUNCT ijassa-713 220 1 berlin berlin PROPN ijassa-713 220 2 : : PUNCT ijassa-713 220 3 springer springer NOUN ijassa-713 220 4 verlag verlag PROPN ijassa-713 220 5 . . PUNCT ijassa-713 221 1 [ [ X ijassa-713 221 2 11 11 NUM ijassa-713 221 3 ] ] X ijassa-713 221 4 liu liu PROPN ijassa-713 221 5 , , PUNCT ijassa-713 221 6 b. b. PROPN ijassa-713 221 7 ( ( PUNCT ijassa-713 221 8 2016 2016 NUM ijassa-713 221 9 ) ) PUNCT ijassa-713 221 10 . . PUNCT ijassa-713 222 1 uncertain uncertain ADJ ijassa-713 222 2 theory theory NOUN ijassa-713 222 3 ( ( PUNCT ijassa-713 222 4 5th 5th ADJ ijassa-713 222 5 ed ed NOUN ijassa-713 222 6 . . PUNCT ijassa-713 222 7 ) ) PUNCT ijassa-713 222 8 . . PUNCT ijassa-713 223 1 china china PROPN ijassa-713 223 2 : : PUNCT ijassa-713 224 1 uncertainty uncertainty NOUN ijassa-713 224 2 theory theory NOUN ijassa-713 224 3 laboratory laboratory NOUN ijassa-713 224 4 . . PUNCT ijassa-713 225 1 [ [ X ijassa-713 225 2 12 12 NUM ijassa-713 225 3 ] ] SYM ijassa-713 225 4 merton merton PROPN ijassa-713 225 5 , , PUNCT ijassa-713 225 6 r. r. PROPN ijassa-713 225 7 c. c. PROPN ijassa-713 225 8 ( ( PUNCT ijassa-713 225 9 1971 1971 NUM ijassa-713 225 10 ) ) PUNCT ijassa-713 225 11 . . PUNCT ijassa-713 226 1 optimal optimal ADJ ijassa-713 226 2 consumption consumption NOUN ijassa-713 226 3 and and CCONJ ijassa-713 226 4 portfolio portfolio NOUN ijassa-713 226 5 rules rule NOUN ijassa-713 226 6 in in ADP ijassa-713 226 7 a a DET ijassa-713 226 8 continuous continuous ADJ ijassa-713 226 9 time time NOUN ijassa-713 226 10 model model NOUN ijassa-713 226 11 . . PUNCT ijassa-713 227 1 journal journal PROPN ijassa-713 227 2 of of ADP ijassa-713 227 3 economic economic ADJ ijassa-713 227 4 theory theory NOUN ijassa-713 227 5 , , PUNCT ijassa-713 227 6 42(3 42(3 NUM ijassa-713 227 7 ) ) PUNCT ijassa-713 227 8 , , PUNCT ijassa-713 227 9 373 373 NUM ijassa-713 227 10 - - SYM ijassa-713 227 11 413 413 NUM ijassa-713 227 12 . . PUNCT ijassa-713 228 1 [ [ X ijassa-713 228 2 13 13 NUM ijassa-713 228 3 ] ] X ijassa-713 228 4 miller miller PROPN ijassa-713 228 5 , , PUNCT ijassa-713 228 6 m. m. NOUN ijassa-713 228 7 & & CCONJ ijassa-713 228 8 scholes scholes PROPN ijassa-713 228 9 , , PUNCT ijassa-713 228 10 m. m. NOUN ijassa-713 228 11 ( ( PUNCT ijassa-713 228 12 1972 1972 NUM ijassa-713 228 13 ) ) PUNCT ijassa-713 228 14 . . PUNCT ijassa-713 229 1 rates rate NOUN ijassa-713 229 2 of of ADP ijassa-713 229 3 return return NOUN ijassa-713 229 4 in in ADP ijassa-713 229 5 relation relation NOUN ijassa-713 229 6 to to PART ijassa-713 229 7 risk risk VERB ijassa-713 229 8 : : PUNCT ijassa-713 229 9 a a DET ijassa-713 229 10 reexamination reexamination NOUN ijassa-713 229 11 of of ADP ijassa-713 229 12 some some DET ijassa-713 229 13 recent recent ADJ ijassa-713 229 14 findings finding NOUN ijassa-713 229 15 . . PUNCT ijassa-713 230 1 studies study NOUN ijassa-713 230 2 in in ADP ijassa-713 230 3 the the DET ijassa-713 230 4 theory theory NOUN ijassa-713 230 5 of of ADP ijassa-713 230 6 capital capital NOUN ijassa-713 230 7 markets market NOUN ijassa-713 230 8 , , PUNCT ijassa-713 230 9 michael michael PROPN ijassa-713 230 10 c. c. PROPN ijassa-713 230 11 jensen jensen PROPN ijassa-713 230 12 , , PUNCT ijassa-713 230 13 ed ed NOUN ijassa-713 230 14 . . PROPN ijassa-713 230 15 , , PUNCT ijassa-713 230 16 praeger praeger NOUN ijassa-713 230 17 , , PUNCT ijassa-713 230 18 new new PROPN ijassa-713 230 19 york york PROPN ijassa-713 230 20 , , PUNCT ijassa-713 230 21 47 47 NUM ijassa-713 230 22 - - SYM ijassa-713 230 23 78 78 NUM ijassa-713 230 24 . . PUNCT ijassa-713 231 1 [ [ X ijassa-713 231 2 14 14 NUM ijassa-713 231 3 ] ] SYM ijassa-713 231 4 stambaugh stambaugh NOUN ijassa-713 231 5 , , PUNCT ijassa-713 231 6 r. r. PROPN ijassa-713 231 7 f. f. PROPN ijassa-713 231 8 ( ( PUNCT ijassa-713 231 9 1982 1982 NUM ijassa-713 231 10 ) ) PUNCT ijassa-713 231 11 . . PUNCT ijassa-713 232 1 on on ADP ijassa-713 232 2 the the DET ijassa-713 232 3 exclusion exclusion NOUN ijassa-713 232 4 of of ADP ijassa-713 232 5 assets asset NOUN ijassa-713 232 6 from from ADP ijassa-713 232 7 tests test NOUN ijassa-713 232 8 of of ADP ijassa-713 232 9 two two NUM ijassa-713 232 10 - - PUNCT ijassa-713 232 11 parameter parameter NOUN ijassa-713 232 12 model model NOUN ijassa-713 232 13 : : PUNCT ijassa-713 232 14 a a DET ijassa-713 232 15 sensitivity sensitivity NOUN ijassa-713 232 16 analysis analysis NOUN ijassa-713 232 17 . . PUNCT ijassa-713 233 1 journal journal NOUN ijassa-713 233 2 of of ADP ijassa-713 233 3 financial financial ADJ ijassa-713 233 4 economics economic NOUN ijassa-713 233 5 , , PUNCT ijassa-713 233 6 10(3 10(3 NUM ijassa-713 233 7 ) ) PUNCT ijassa-713 233 8 , , PUNCT ijassa-713 233 9 237 237 NUM ijassa-713 233 10 - - SYM ijassa-713 233 11 268 268 NUM ijassa-713 233 12 . . PUNCT ijassa-713 234 1 [ [ X ijassa-713 234 2 15 15 NUM ijassa-713 234 3 ] ] X ijassa-713 234 4 stein stein PROPN ijassa-713 234 5 , , PUNCT ijassa-713 234 6 j. j. PROPN ijassa-713 234 7 l. l. PROPN ijassa-713 234 8 ( ( PUNCT ijassa-713 234 9 2003 2003 NUM ijassa-713 234 10 ) ) PUNCT ijassa-713 234 11 . . PUNCT ijassa-713 235 1 stochastic stochastic ADJ ijassa-713 235 2 optimal optimal ADJ ijassa-713 235 3 control control NOUN ijassa-713 235 4 modelling modelling NOUN ijassa-713 235 5 of of ADP ijassa-713 235 6 debt debt NOUN ijassa-713 235 7 crises crisis NOUN ijassa-713 235 8 . . PUNCT ijassa-713 236 1 cesifo cesifo PROPN ijassa-713 236 2 ( ( PUNCT ijassa-713 236 3 working work VERB ijassa-713 236 4 paper paper NOUN ijassa-713 236 5 1043 1043 NUM ijassa-713 236 6 ) ) PUNCT ijassa-713 236 7 , , PUNCT ijassa-713 236 8 1 1 NUM ijassa-713 236 9 - - SYM ijassa-713 236 10 23 23 NUM ijassa-713 236 11 . . PUNCT ijassa-713 237 1 [ [ X ijassa-713 237 2 16 16 NUM ijassa-713 237 3 ] ] X ijassa-713 237 4 yao yao PROPN ijassa-713 237 5 , , PUNCT ijassa-713 237 6 k. k. PROPN ijassa-713 237 7 & & CCONJ ijassa-713 237 8 chen chen PROPN ijassa-713 237 9 , , PUNCT ijassa-713 237 10 x. x. PROPN ijassa-713 237 11 ( ( PUNCT ijassa-713 237 12 2013 2013 NUM ijassa-713 237 13 ) ) PUNCT ijassa-713 237 14 . . PUNCT ijassa-713 238 1 a a DET ijassa-713 238 2 numerical numerical ADJ ijassa-713 238 3 method method NOUN ijassa-713 238 4 for for ADP ijassa-713 238 5 solving solve VERB ijassa-713 238 6 uncertain uncertain ADJ ijassa-713 238 7 differential differential ADJ ijassa-713 238 8 equations equation NOUN ijassa-713 238 9 . . PUNCT ijassa-713 239 1 journal journal NOUN ijassa-713 239 2 of of ADP ijassa-713 239 3 intelligent intelligent ADJ ijassa-713 239 4 fuzzy fuzzy ADJ ijassa-713 239 5 systems system NOUN ijassa-713 239 6 , , PUNCT ijassa-713 239 7 25(3 25(3 NUM ijassa-713 239 8 ) ) PUNCT ijassa-713 239 9 , , PUNCT ijassa-713 239 10 825 825 NUM ijassa-713 239 11 - - SYM ijassa-713 239 12 832 832 NUM ijassa-713 239 13 . . PUNCT ijassa-713 240 1 [ [ X ijassa-713 240 2 17 17 NUM ijassa-713 240 3 ] ] X ijassa-713 240 4 yang yang PROPN ijassa-713 240 5 , , PUNCT ijassa-713 240 6 x. x. PROPN ijassa-713 240 7 & & CCONJ ijassa-713 240 8 shen shen PROPN ijassa-713 240 9 , , PUNCT ijassa-713 240 10 y.(2015 y.(2015 PROPN ijassa-713 240 11 ) ) PUNCT ijassa-713 240 12 . . PUNCT ijassa-713 241 1 runge runge NOUN ijassa-713 241 2 - - PUNCT ijassa-713 241 3 kutta kutta NOUN ijassa-713 241 4 method method NOUN ijassa-713 241 5 for for ADP ijassa-713 241 6 solving solve VERB ijassa-713 241 7 uncertain uncertain ADJ ijassa-713 241 8 differential differential ADJ ijassa-713 241 9 equations equation NOUN ijassa-713 241 10 , , PUNCT ijassa-713 241 11 journal journal NOUN ijassa-713 241 12 of of ADP ijassa-713 241 13 uncertainty uncertainty NOUN ijassa-713 241 14 analysis analysis NOUN ijassa-713 241 15 and and CCONJ ijassa-713 241 16 applications application NOUN ijassa-713 241 17 , , PUNCT ijassa-713 241 18 3(17 3(17 NUM ijassa-713 241 19 ) ) PUNCT ijassa-713 241 20 , , PUNCT ijassa-713 241 21 1 1 NUM ijassa-713 241 22 - - SYM ijassa-713 241 23 12 12 NUM ijassa-713 241 24 . . PUNCT ijassa-713 242 1 [ [ X ijassa-713 242 2 18 18 NUM ijassa-713 242 3 ] ] SYM ijassa-713 242 4 yao yao NOUN ijassa-713 242 5 , , PUNCT ijassa-713 242 6 k. k. PROPN ijassa-713 242 7 ( ( PUNCT ijassa-713 242 8 2013 2013 NUM ijassa-713 242 9 ) ) PUNCT ijassa-713 242 10 . . PUNCT ijassa-713 243 1 extreme extreme ADJ ijassa-713 243 2 values value NOUN ijassa-713 243 3 and and CCONJ ijassa-713 243 4 integral integral ADJ ijassa-713 243 5 of of ADP ijassa-713 243 6 solution solution NOUN ijassa-713 243 7 of of ADP ijassa-713 243 8 uncertain uncertain ADJ ijassa-713 243 9 differential differential ADJ ijassa-713 243 10 equation equation NOUN ijassa-713 243 11 . . PUNCT ijassa-713 244 1 journal journal NOUN ijassa-713 244 2 of of ADP ijassa-713 244 3 uncertainty uncertainty NOUN ijassa-713 244 4 analysis analysis NOUN ijassa-713 244 5 and and CCONJ ijassa-713 244 6 applications application NOUN ijassa-713 244 7 , , PUNCT ijassa-713 244 8 1(2 1(2 NUM ijassa-713 244 9 ) ) PUNCT ijassa-713 244 10 , , PUNCT ijassa-713 244 11 1 1 NUM ijassa-713 244 12 - - SYM ijassa-713 244 13 21 21 NUM ijassa-713 244 14 . . PUNCT ijassa-713 245 1 [ [ X ijassa-713 245 2 19 19 NUM ijassa-713 245 3 ] ] X ijassa-713 245 4 zhu zhu PROPN ijassa-713 245 5 , , PUNCT ijassa-713 245 6 y. y. PROPN ijassa-713 245 7 ( ( PUNCT ijassa-713 245 8 2010 2010 NUM ijassa-713 245 9 ) ) PUNCT ijassa-713 245 10 . . PUNCT ijassa-713 246 1 uncertain uncertain ADJ ijassa-713 246 2 optimal optimal ADJ ijassa-713 246 3 control control NOUN ijassa-713 246 4 with with ADP ijassa-713 246 5 application application NOUN ijassa-713 246 6 to to ADP ijassa-713 246 7 a a DET ijassa-713 246 8 portfolio portfolio NOUN ijassa-713 246 9 selection selection NOUN ijassa-713 246 10 model model NOUN ijassa-713 246 11 . . PUNCT ijassa-713 247 1 cybernetics cybernetic NOUN ijassa-713 247 2 and and CCONJ ijassa-713 247 3 systems system NOUN ijassa-713 247 4 : : PUNCT ijassa-713 247 5 an an DET ijassa-713 247 6 international international ADJ ijassa-713 247 7 journal journal NOUN ijassa-713 247 8 , , PUNCT ijassa-713 247 9 41 41 NUM ijassa-713 247 10 , , PUNCT ijassa-713 247 11 535 535 NUM ijassa-713 247 12 - - SYM ijassa-713 247 13 547 547 NUM ijassa-713 247 14 . . PUNCT