id sid tid token lemma pos cana-3678 1 1 communications communication NOUN cana-3678 1 2 on on ADP cana-3678 1 3 applied apply VERB cana-3678 1 4 nonlinear nonlinear ADJ cana-3678 1 5 analysis analysis NOUN cana-3678 1 6 issn issn NOUN cana-3678 1 7 : : PUNCT cana-3678 1 8 1074 1074 NUM cana-3678 1 9 - - PUNCT cana-3678 1 10 133x 133x NUM cana-3678 1 11 vol vol NOUN cana-3678 1 12 32 32 NUM cana-3678 1 13 no no NOUN cana-3678 1 14 . . PUNCT cana-3678 2 1 8s 8s PROPN cana-3678 2 2 ( ( PUNCT cana-3678 2 3 2025 2025 NUM cana-3678 2 4 ) ) PUNCT cana-3678 2 5 320 320 NUM cana-3678 2 6 https://internationalpubls.com https://internationalpubls.com X cana-3678 2 7 deep deep ADJ cana-3678 2 8 learning learning NOUN cana-3678 2 9 for for ADP cana-3678 2 10 non non ADJ cana-3678 2 11 - - ADJ cana-3678 2 12 linear linear ADJ cana-3678 2 13 black black ADJ cana-3678 2 14 - - PUNCT cana-3678 2 15 scholes schole NOUN cana-3678 2 16 model model NOUN cana-3678 2 17 in in ADP cana-3678 2 18 an an DET cana-3678 2 19 illiquid illiquid ADJ cana-3678 2 20 financial financial ADJ cana-3678 2 21 market market NOUN cana-3678 2 22 with with ADP cana-3678 2 23 transaction transaction NOUN cana-3678 2 24 costs cost NOUN cana-3678 2 25 tejal tejal ADV cana-3678 2 26 shah1 shah1 NOUN cana-3678 2 27 , , PUNCT cana-3678 2 28 jaita jaita PROPN cana-3678 2 29 sharma2 sharma2 NOUN cana-3678 3 1 1department 1department NUM cana-3678 3 2 of of ADP cana-3678 3 3 applied apply VERB cana-3678 3 4 mathematics mathematic NOUN cana-3678 3 5 , , PUNCT cana-3678 3 6 faculty faculty NOUN cana-3678 3 7 of of ADP cana-3678 3 8 technology technology NOUN cana-3678 3 9 and and CCONJ cana-3678 3 10 engineering engineering NOUN cana-3678 3 11 , , PUNCT cana-3678 3 12 the the DET cana-3678 3 13 maharaja maharaja PROPN cana-3678 3 14 sayajirao sayajirao PROPN cana-3678 3 15 university university PROPN cana-3678 3 16 of of ADP cana-3678 3 17 baroda baroda PROPN cana-3678 3 18 , , PUNCT cana-3678 3 19 vadodara vadodara NOUN cana-3678 3 20 , , PUNCT cana-3678 3 21 india india PROPN cana-3678 3 22 . . PUNCT cana-3678 4 1 ( ( PUNCT cana-3678 4 2 e e NOUN cana-3678 4 3 - - NOUN cana-3678 4 4 mail mail NOUN cana-3678 4 5 : : PUNCT cana-3678 4 6 shahtejal11@gmail.com shahtejal11@gmail.com X cana-3678 4 7 ) ) PUNCT cana-3678 4 8 2department 2department NUM cana-3678 4 9 of of ADP cana-3678 4 10 applied apply VERB cana-3678 4 11 mathematics mathematic NOUN cana-3678 4 12 , , PUNCT cana-3678 4 13 faculty faculty NOUN cana-3678 4 14 of of ADP cana-3678 4 15 technology technology NOUN cana-3678 4 16 and and CCONJ cana-3678 4 17 engineering engineering NOUN cana-3678 4 18 , , PUNCT cana-3678 4 19 the the DET cana-3678 4 20 maharaja maharaja PROPN cana-3678 4 21 sayajirao sayajirao PROPN cana-3678 4 22 university university PROPN cana-3678 4 23 of of ADP cana-3678 4 24 baroda baroda PROPN cana-3678 4 25 , , PUNCT cana-3678 4 26 vadodara vadodara NOUN cana-3678 4 27 , , PUNCT cana-3678 4 28 india india PROPN cana-3678 4 29 . . PUNCT cana-3678 5 1 ( ( PUNCT cana-3678 5 2 e e NOUN cana-3678 5 3 - - NOUN cana-3678 5 4 mail mail NOUN cana-3678 5 5 : : PUNCT cana-3678 5 6 jaita.sharma-appmath@msubaroda.ac.in jaita.sharma-appmath@msubaroda.ac.in X cana-3678 5 7 ) ) PUNCT cana-3678 5 8 article article NOUN cana-3678 5 9 history history NOUN cana-3678 5 10 : : PUNCT cana-3678 5 11 received receive VERB cana-3678 5 12 : : PUNCT cana-3678 5 13 27 27 NUM cana-3678 5 14 - - SYM cana-3678 5 15 10 10 NUM cana-3678 5 16 - - PUNCT cana-3678 5 17 2024 2024 NUM cana-3678 5 18 revised:26 revised:26 ADJ cana-3678 5 19 - - SYM cana-3678 5 20 11 11 NUM cana-3678 5 21 - - PUNCT cana-3678 5 22 2024 2024 NUM cana-3678 5 23 accepted:28 accepted:28 NUM cana-3678 5 24 - - PUNCT cana-3678 5 25 12 12 NUM cana-3678 5 26 - - PUNCT cana-3678 5 27 2024 2024 NUM cana-3678 5 28 abstract abstract NOUN cana-3678 5 29 : : PUNCT cana-3678 5 30 a a DET cana-3678 5 31 topic topic NOUN cana-3678 5 32 of of ADP cana-3678 5 33 interest interest NOUN cana-3678 5 34 in in ADP cana-3678 5 35 financial financial ADJ cana-3678 5 36 mathematics mathematic NOUN cana-3678 5 37 is be AUX cana-3678 5 38 the the DET cana-3678 5 39 black black ADJ cana-3678 5 40 - - PUNCT cana-3678 5 41 scholes schole NOUN cana-3678 5 42 model model NOUN cana-3678 5 43 . . PUNCT cana-3678 6 1 however however ADV cana-3678 6 2 , , PUNCT cana-3678 6 3 the the DET cana-3678 6 4 underlying underlie VERB cana-3678 6 5 asset asset NOUN cana-3678 6 6 price price NOUN cana-3678 6 7 in in ADP cana-3678 6 8 the the DET cana-3678 6 9 stock stock NOUN cana-3678 6 10 market market NOUN cana-3678 6 11 may may AUX cana-3678 6 12 not not PART cana-3678 6 13 be be AUX cana-3678 6 14 satisfied satisfied ADJ cana-3678 6 15 by by ADP cana-3678 6 16 this this DET cana-3678 6 17 linear linear ADJ cana-3678 6 18 model model NOUN cana-3678 6 19 , , PUNCT cana-3678 6 20 which which PRON cana-3678 6 21 was be AUX cana-3678 6 22 developed develop VERB cana-3678 6 23 under under ADP cana-3678 6 24 a a DET cana-3678 6 25 number number NOUN cana-3678 6 26 of of ADP cana-3678 6 27 assumptions assumption NOUN cana-3678 6 28 , , PUNCT cana-3678 6 29 including include VERB cana-3678 6 30 liquidity liquidity NOUN cana-3678 6 31 and and CCONJ cana-3678 6 32 the the DET cana-3678 6 33 absence absence NOUN cana-3678 6 34 of of ADP cana-3678 6 35 transaction transaction NOUN cana-3678 6 36 costs cost NOUN cana-3678 6 37 . . PUNCT cana-3678 7 1 the the DET cana-3678 7 2 linear linear PROPN cana-3678 7 3 model model NOUN cana-3678 7 4 has have AUX cana-3678 7 5 restricted restrict VERB cana-3678 7 6 its its PRON cana-3678 7 7 precision precision NOUN cana-3678 7 8 in in ADP cana-3678 7 9 actual actual ADJ cana-3678 7 10 market market NOUN cana-3678 7 11 conditions condition NOUN cana-3678 7 12 . . PUNCT cana-3678 8 1 we we PRON cana-3678 8 2 study study VERB cana-3678 8 3 the the DET cana-3678 8 4 transaction transaction NOUN cana-3678 8 5 cost cost NOUN cana-3678 8 6 model model NOUN cana-3678 8 7 for for ADP cana-3678 8 8 modelling model VERB cana-3678 8 9 illiquid illiquid ADJ cana-3678 8 10 markets market NOUN cana-3678 8 11 from from ADP cana-3678 8 12 the the DET cana-3678 8 13 extended extended ADJ cana-3678 8 14 nonlinear nonlinear ADJ cana-3678 8 15 black black ADJ cana-3678 8 16 - - PUNCT cana-3678 8 17 scholes schole NOUN cana-3678 8 18 model model NOUN cana-3678 8 19 . . PUNCT cana-3678 9 1 using use VERB cana-3678 9 2 a a DET cana-3678 9 3 semi semi ADJ cana-3678 9 4 - - ADJ cana-3678 9 5 discretization discretization ADJ cana-3678 9 6 finite finite ADJ cana-3678 9 7 difference difference NOUN cana-3678 9 8 approach approach NOUN cana-3678 9 9 , , PUNCT cana-3678 9 10 the the DET cana-3678 9 11 nonlinear nonlinear ADJ cana-3678 9 12 partial partial ADJ cana-3678 9 13 differential differential NOUN cana-3678 9 14 equation equation NOUN cana-3678 9 15 is be AUX cana-3678 9 16 transformed transform VERB cana-3678 9 17 into into ADP cana-3678 9 18 a a DET cana-3678 9 19 nonlinear nonlinear ADJ cana-3678 9 20 ordinary ordinary ADJ cana-3678 9 21 differential differential ADJ cana-3678 9 22 equation equation NOUN cana-3678 9 23 . . PUNCT cana-3678 10 1 deep deep ADJ cana-3678 10 2 learning learning NOUN cana-3678 10 3 ( ( PUNCT cana-3678 10 4 dl dl INTJ cana-3678 10 5 ) ) PUNCT cana-3678 10 6 is be AUX cana-3678 10 7 an an DET cana-3678 10 8 advanced advanced ADJ cana-3678 10 9 technique technique NOUN cana-3678 10 10 of of ADP cana-3678 10 11 machine machine NOUN cana-3678 10 12 learning learning NOUN cana-3678 10 13 solves solve VERB cana-3678 10 14 the the DET cana-3678 10 15 converted converted ADJ cana-3678 10 16 ordinary ordinary ADJ cana-3678 10 17 differential differential ADJ cana-3678 10 18 equation equation NOUN cana-3678 10 19 by by ADP cana-3678 10 20 fully fully ADV cana-3678 10 21 connected connect VERB cana-3678 10 22 neural neural ADJ cana-3678 10 23 network network NOUN cana-3678 10 24 ( ( PUNCT cana-3678 10 25 fcnn fcnn PROPN cana-3678 10 26 ) ) PUNCT cana-3678 10 27 . . PUNCT cana-3678 11 1 by by ADP cana-3678 11 2 modelling model VERB cana-3678 11 3 the the DET cana-3678 11 4 complex complex ADJ cana-3678 11 5 and and CCONJ cana-3678 11 6 nonlinear nonlinear ADJ cana-3678 11 7 relationships relationship NOUN cana-3678 11 8 among among ADP cana-3678 11 9 market market NOUN cana-3678 11 10 variables variable NOUN cana-3678 11 11 , , PUNCT cana-3678 11 12 dl dl PROPN cana-3678 11 13 models model NOUN cana-3678 11 14 can can AUX cana-3678 11 15 generate generate VERB cana-3678 11 16 option option NOUN cana-3678 11 17 pricing pricing NOUN cana-3678 11 18 forecasts forecast NOUN cana-3678 11 19 that that PRON cana-3678 11 20 are be AUX cana-3678 11 21 more more ADV cana-3678 11 22 dependable dependable ADJ cana-3678 11 23 and and CCONJ cana-3678 11 24 precise precise ADJ cana-3678 11 25 , , PUNCT cana-3678 11 26 not not PART cana-3678 11 27 just just ADV cana-3678 11 28 for for ADP cana-3678 11 29 continuous continuous ADJ cana-3678 11 30 data datum NOUN cana-3678 11 31 but but CCONJ cana-3678 11 32 also also ADV cana-3678 11 33 for for ADP cana-3678 11 34 discontinuous discontinuous ADJ cana-3678 11 35 data datum NOUN cana-3678 11 36 ( ( PUNCT cana-3678 11 37 at at ADP cana-3678 11 38 jump jump NOUN cana-3678 11 39 point point NOUN cana-3678 11 40 ) ) PUNCT cana-3678 11 41 . . PUNCT cana-3678 12 1 introduction introduction NOUN cana-3678 12 2 : : PUNCT cana-3678 12 3 nonlinear nonlinear ADJ cana-3678 12 4 partial partial ADJ cana-3678 12 5 differential differential NOUN cana-3678 12 6 equation equation NOUN cana-3678 12 7 plays play VERB cana-3678 12 8 a a DET cana-3678 12 9 crucial crucial ADJ cana-3678 12 10 role role NOUN cana-3678 12 11 in in ADP cana-3678 12 12 financial financial ADJ cana-3678 12 13 modelling modelling NOUN cana-3678 12 14 , , PUNCT cana-3678 12 15 especially especially ADV cana-3678 12 16 in in ADP cana-3678 12 17 the the DET cana-3678 12 18 pricing pricing NOUN cana-3678 12 19 of of ADP cana-3678 12 20 derivatives derivative NOUN cana-3678 12 21 like like ADP cana-3678 12 22 options option NOUN cana-3678 12 23 . . PUNCT cana-3678 13 1 the the DET cana-3678 13 2 blackscholes blackschole NOUN cana-3678 13 3 model model PROPN cana-3678 13 4 , , PUNCT cana-3678 13 5 introduced introduce VERB cana-3678 13 6 in in ADP cana-3678 13 7 1973 1973 NUM cana-3678 13 8 , , PUNCT cana-3678 13 9 continues continue VERB cana-3678 13 10 to to PART cana-3678 13 11 be be AUX cana-3678 13 12 one one NUM cana-3678 13 13 of of ADP cana-3678 13 14 the the DET cana-3678 13 15 most most ADV cana-3678 13 16 widely widely ADV cana-3678 13 17 used use VERB cana-3678 13 18 frameworks framework NOUN cana-3678 13 19 for for ADP cana-3678 13 20 pricing price VERB cana-3678 13 21 european european ADJ cana-3678 13 22 options option NOUN cana-3678 13 23 . . PUNCT cana-3678 14 1 ho ho PROPN cana-3678 14 2 wever wever PROPN cana-3678 14 3 , , PUNCT cana-3678 14 4 this this DET cana-3678 14 5 model model NOUN cana-3678 14 6 is be AUX cana-3678 14 7 a a DET cana-3678 14 8 linear linear ADJ cana-3678 14 9 one one NUM cana-3678 14 10 and and CCONJ cana-3678 14 11 offers offer VERB cana-3678 14 12 an an DET cana-3678 14 13 analytical analytical ADJ cana-3678 14 14 solution solution NOUN cana-3678 14 15 , , PUNCT cana-3678 14 16 yet yet CCONJ cana-3678 14 17 it it PRON cana-3678 14 18 is be AUX cana-3678 14 19 not not PART cana-3678 14 20 appropriate appropriate ADJ cana-3678 14 21 for for ADP cana-3678 14 22 the the DET cana-3678 14 23 complexities complexity NOUN cana-3678 14 24 of of ADP cana-3678 14 25 real real ADJ cana-3678 14 26 market market NOUN cana-3678 14 27 assumptions assumption NOUN cana-3678 14 28 that that PRON cana-3678 14 29 exhibit exhibit VERB cana-3678 14 30 nonlinear nonlinear ADJ cana-3678 14 31 effects effect NOUN cana-3678 14 32 . . PUNCT cana-3678 15 1 we we PRON cana-3678 15 2 examine examine VERB cana-3678 15 3 the the DET cana-3678 15 4 transaction transaction NOUN cana-3678 15 5 cost cost NOUN cana-3678 15 6 model model NOUN cana-3678 15 7 for for ADP cana-3678 15 8 modelling model VERB cana-3678 15 9 illiquid illiquid ADJ cana-3678 15 10 markets market NOUN cana-3678 15 11 from from ADP cana-3678 15 12 the the DET cana-3678 15 13 extended extended ADJ cana-3678 15 14 nonlinear nonlinear ADJ cana-3678 15 15 black black ADJ cana-3678 15 16 - - PUNCT cana-3678 15 17 scholes schole NOUN cana-3678 15 18 model model NOUN cana-3678 15 19 created create VERB cana-3678 15 20 by by ADP cana-3678 15 21 seelama seelama NOUN cana-3678 15 22 et et PROPN cana-3678 15 23 al al PROPN cana-3678 15 24 . . PROPN cana-3678 16 1 ( ( PUNCT cana-3678 16 2 2021 2021 NUM cana-3678 16 3 ) ) PUNCT cana-3678 16 4 . . PUNCT cana-3678 17 1 first first ADV cana-3678 17 2 using use VERB cana-3678 17 3 a a DET cana-3678 17 4 semi semi ADJ cana-3678 17 5 - - ADJ cana-3678 17 6 discretization discretization ADJ cana-3678 17 7 finite finite ADJ cana-3678 17 8 difference difference NOUN cana-3678 17 9 approach approach NOUN cana-3678 17 10 , , PUNCT cana-3678 17 11 the the DET cana-3678 17 12 nonlinear nonlinear ADJ cana-3678 17 13 partial partial ADJ cana-3678 17 14 differential differential NOUN cana-3678 17 15 equation equation NOUN cana-3678 17 16 is be AUX cana-3678 17 17 transformed transform VERB cana-3678 17 18 into into ADP cana-3678 17 19 a a DET cana-3678 17 20 nonlinear nonlinear ADJ cana-3678 17 21 ordinary ordinary ADJ cana-3678 17 22 differential differential ADJ cana-3678 17 23 equation equation NOUN cana-3678 17 24 . . PUNCT cana-3678 18 1 solves solve VERB cana-3678 18 2 the the DET cana-3678 18 3 converted converted ADJ cana-3678 18 4 ordinary ordinary ADJ cana-3678 18 5 differential differential ADJ cana-3678 18 6 equation equation NOUN cana-3678 18 7 by by ADP cana-3678 18 8 deep deep ADJ cana-3678 18 9 learning learning NOUN cana-3678 18 10 ( ( PUNCT cana-3678 18 11 dl dl NOUN cana-3678 18 12 ) ) PUNCT cana-3678 18 13 based base VERB cana-3678 18 14 fully fully ADV cana-3678 18 15 connected connect VERB cana-3678 18 16 neural neural ADJ cana-3678 18 17 network network NOUN cana-3678 18 18 ( ( PUNCT cana-3678 18 19 fcnn fcnn ADJ cana-3678 18 20 ) ) PUNCT cana-3678 18 21 algorithm algorithm NOUN cana-3678 18 22 . . PUNCT cana-3678 19 1 this this DET cana-3678 19 2 algorithm algorithm NOUN cana-3678 19 3 is be AUX cana-3678 19 4 capable capable ADJ cana-3678 19 5 of of ADP cana-3678 19 6 handling handle VERB cana-3678 19 7 the the DET cana-3678 19 8 nonlinear nonlinear ADJ cana-3678 19 9 behaviour behaviour NOUN cana-3678 19 10 of of ADP cana-3678 19 11 model model NOUN cana-3678 19 12 and and CCONJ cana-3678 19 13 produce produce VERB cana-3678 19 14 more more ADV cana-3678 19 15 accurate accurate ADJ cana-3678 19 16 option option NOUN cana-3678 19 17 value value NOUN cana-3678 19 18 for for ADP cana-3678 19 19 european european ADJ cana-3678 19 20 call call NOUN cana-3678 19 21 . . PUNCT cana-3678 20 1 objectives objective NOUN cana-3678 20 2 : : PUNCT cana-3678 20 3 find find VERB cana-3678 20 4 the the DET cana-3678 20 5 solution solution NOUN cana-3678 20 6 of of ADP cana-3678 20 7 more more ADV cana-3678 20 8 realistic realistic ADJ cana-3678 20 9 nonlinear nonlinear ADJ cana-3678 20 10 model model NOUN cana-3678 20 11 of of ADP cana-3678 20 12 black black ADJ cana-3678 20 13 - - PUNCT cana-3678 20 14 scholes schole NOUN cana-3678 20 15 equation equation NOUN cana-3678 20 16 include include VERB cana-3678 20 17 transaction transaction NOUN cana-3678 20 18 cost cost NOUN cana-3678 20 19 in in ADP cana-3678 20 20 illiquid illiquid ADJ cana-3678 20 21 market market NOUN cana-3678 20 22 with with ADP cana-3678 20 23 deep deep ADJ cana-3678 20 24 learning learning NOUN cana-3678 20 25 algorithm algorithm NOUN cana-3678 20 26 for for ADP cana-3678 20 27 a a DET cana-3678 20 28 european european ADJ cana-3678 20 29 call call NOUN cana-3678 20 30 option option NOUN cana-3678 20 31 . . PUNCT cana-3678 21 1 methods method NOUN cana-3678 21 2 : : PUNCT cana-3678 21 3 from from ADP cana-3678 21 4 extended extended ADJ cana-3678 21 5 nonlinear nonlinear ADJ cana-3678 21 6 black black ADJ cana-3678 21 7 - - PUNCT cana-3678 21 8 scholes schole NOUN cana-3678 21 9 model model NOUN cana-3678 21 10 , , PUNCT cana-3678 21 11 the the DET cana-3678 21 12 nonlinear nonlinear ADJ cana-3678 21 13 model model NOUN cana-3678 21 14 of of ADP cana-3678 21 15 transaction transaction NOUN cana-3678 21 16 cost cost NOUN cana-3678 21 17 in in ADP cana-3678 21 18 illiquid illiquid ADJ cana-3678 21 19 market market NOUN cana-3678 21 20 is be AUX cana-3678 21 21 considered consider VERB cana-3678 21 22 for for ADP cana-3678 21 23 study study NOUN cana-3678 21 24 . . PUNCT cana-3678 22 1 the the DET cana-3678 22 2 nonlinear nonlinear ADJ cana-3678 22 3 partial partial ADJ cana-3678 22 4 differential differential NOUN cana-3678 22 5 equation equation NOUN cana-3678 22 6 is be AUX cana-3678 22 7 converted convert VERB cana-3678 22 8 into into ADP cana-3678 22 9 a a DET cana-3678 22 10 nonlinear nonlinear ADJ cana-3678 22 11 ordinary ordinary ADJ cana-3678 22 12 differential differential ADJ cana-3678 22 13 equation equation NOUN cana-3678 22 14 by by ADP cana-3678 22 15 semi semi ADJ cana-3678 22 16 - - ADJ cana-3678 22 17 discretization discretization ADJ cana-3678 22 18 finite finite ADJ cana-3678 22 19 difference difference NOUN cana-3678 22 20 method method NOUN cana-3678 22 21 . . PUNCT cana-3678 23 1 dl dl PROPN cana-3678 23 2 is be AUX cana-3678 23 3 a a DET cana-3678 23 4 sophisticated sophisticated ADJ cana-3678 23 5 machine machine NOUN cana-3678 23 6 learning learning NOUN cana-3678 23 7 technique technique NOUN cana-3678 23 8 that that PRON cana-3678 23 9 solves solve NOUN cana-3678 23 10 transformed transform VERB cana-3678 23 11 ordinary ordinary ADJ cana-3678 23 12 differential differential ADJ cana-3678 23 13 equations equation NOUN cana-3678 23 14 using use VERB cana-3678 23 15 fully fully ADV cana-3678 23 16 connected connect VERB cana-3678 23 17 neural neural ADJ cana-3678 23 18 network network NOUN cana-3678 23 19 ( ( PUNCT cana-3678 23 20 fcnn fcnn ADJ cana-3678 23 21 ) ) PUNCT cana-3678 23 22 algorithm algorithm NOUN cana-3678 23 23 . . PUNCT cana-3678 24 1 dl dl PROPN cana-3678 24 2 algorithm algorithm PROPN cana-3678 24 3 uses use VERB cana-3678 24 4 a a DET cana-3678 24 5 python python NOUN cana-3678 24 6 program program NOUN cana-3678 24 7 . . PUNCT cana-3678 25 1 results result NOUN cana-3678 25 2 : : PUNCT cana-3678 25 3 for for ADP cana-3678 25 4 european european ADJ cana-3678 25 5 call call NOUN cana-3678 25 6 option option NOUN cana-3678 25 7 , , PUNCT cana-3678 25 8 option option NOUN cana-3678 25 9 values value NOUN cana-3678 25 10 are be AUX cana-3678 25 11 predicted predict VERB cana-3678 25 12 for for ADP cana-3678 25 13 different different ADJ cana-3678 25 14 number number NOUN cana-3678 25 15 of of ADP cana-3678 25 16 neurons neuron NOUN cana-3678 25 17 with with ADP cana-3678 25 18 different different ADJ cana-3678 25 19 loss loss NOUN cana-3678 25 20 functions function NOUN cana-3678 25 21 like like ADP cana-3678 25 22 mse mse NOUN cana-3678 25 23 and and CCONJ cana-3678 25 24 mae mae PROPN cana-3678 25 25 at at ADP cana-3678 25 26 the the DET cana-3678 25 27 time time NOUN cana-3678 25 28 of of ADP cana-3678 25 29 maturity maturity NOUN cana-3678 25 30 . . PUNCT cana-3678 26 1 graphical graphical ADJ cana-3678 26 2 communications communication NOUN cana-3678 26 3 on on ADP cana-3678 26 4 applied apply VERB cana-3678 26 5 nonlinear nonlinear ADJ cana-3678 26 6 analysis analysis NOUN cana-3678 26 7 issn issn NOUN cana-3678 26 8 : : PUNCT cana-3678 26 9 1074 1074 NUM cana-3678 26 10 - - PUNCT cana-3678 26 11 133x 133x NUM cana-3678 26 12 vol vol NOUN cana-3678 26 13 32 32 NUM cana-3678 26 14 no no NOUN cana-3678 26 15 . . PUNCT cana-3678 27 1 8s 8s PROPN cana-3678 27 2 ( ( PUNCT cana-3678 27 3 2025 2025 NUM cana-3678 27 4 ) ) PUNCT cana-3678 27 5 321 321 NUM cana-3678 27 6 https://internationalpubls.com https://internationalpubls.com X cana-3678 27 7 representation representation NOUN cana-3678 27 8 shows show VERB cana-3678 27 9 the the DET cana-3678 27 10 accuracy accuracy NOUN cana-3678 27 11 of of ADP cana-3678 27 12 the the DET cana-3678 27 13 algorithm algorithm NOUN cana-3678 27 14 at at ADP cana-3678 27 15 continuous continuous ADJ cana-3678 27 16 as as ADV cana-3678 27 17 well well ADV cana-3678 27 18 as as ADP cana-3678 27 19 at at ADP cana-3678 27 20 jump jump NOUN cana-3678 27 21 point point NOUN cana-3678 27 22 ( ( PUNCT cana-3678 27 23 strike strike NOUN cana-3678 27 24 price price NOUN cana-3678 27 25 ) ) PUNCT cana-3678 27 26 . . PUNCT cana-3678 28 1 conclusions conclusion NOUN cana-3678 28 2 : : PUNCT cana-3678 28 3 the the DET cana-3678 28 4 method method NOUN cana-3678 28 5 of of ADP cana-3678 28 6 solving solve VERB cana-3678 28 7 a a DET cana-3678 28 8 complex complex ADJ cana-3678 28 9 nonlinear nonlinear ADJ cana-3678 28 10 partial partial ADJ cana-3678 28 11 differential differential NOUN cana-3678 28 12 equation equation NOUN cana-3678 28 13 by by ADP cana-3678 28 14 transforming transform VERB cana-3678 28 15 it it PRON cana-3678 28 16 into into ADP cana-3678 28 17 a a DET cana-3678 28 18 nonlinear nonlinear ADJ cana-3678 28 19 ordinary ordinary ADJ cana-3678 28 20 differential differential ADJ cana-3678 28 21 equation equation NOUN cana-3678 28 22 is be AUX cana-3678 28 23 valuable valuable ADJ cana-3678 28 24 . . PUNCT cana-3678 29 1 more more ADV cana-3678 29 2 precise precise ADJ cana-3678 29 3 pricing pricing NOUN cana-3678 29 4 estimates estimate NOUN cana-3678 29 5 for for ADP cana-3678 29 6 option option NOUN cana-3678 29 7 values value NOUN cana-3678 29 8 with with ADP cana-3678 29 9 nonlinear nonlinear ADJ cana-3678 29 10 effects effect NOUN cana-3678 29 11 in in ADP cana-3678 29 12 financial financial ADJ cana-3678 29 13 data datum NOUN cana-3678 29 14 could could AUX cana-3678 29 15 be be AUX cana-3678 29 16 improved improve VERB cana-3678 29 17 by by ADP cana-3678 29 18 deep deep ADJ cana-3678 29 19 learning learning NOUN cana-3678 29 20 . . PUNCT cana-3678 30 1 keywords keyword NOUN cana-3678 30 2 : : PUNCT cana-3678 30 3 nonlinear nonlinear ADJ cana-3678 30 4 black black ADJ cana-3678 30 5 - - PUNCT cana-3678 30 6 scholes schole NOUN cana-3678 30 7 equation equation NOUN cana-3678 30 8 , , PUNCT cana-3678 30 9 transaction transaction NOUN cana-3678 30 10 costs cost NOUN cana-3678 30 11 , , PUNCT cana-3678 30 12 illiquid illiquid ADJ cana-3678 30 13 markets market NOUN cana-3678 30 14 , , PUNCT cana-3678 30 15 deep deep ADJ cana-3678 30 16 learning learning NOUN cana-3678 30 17 . . PUNCT cana-3678 31 1 1 1 X cana-3678 31 2 . . X cana-3678 31 3 introduction introduction NOUN cana-3678 31 4 derivatives derivative NOUN cana-3678 31 5 are be AUX cana-3678 31 6 financial financial ADJ cana-3678 31 7 tools tool NOUN cana-3678 31 8 that that PRON cana-3678 31 9 provide provide VERB cana-3678 31 10 the the DET cana-3678 31 11 option option NOUN cana-3678 31 12 to to PART cana-3678 31 13 purchase purchase VERB cana-3678 31 14 or or CCONJ cana-3678 31 15 sell sell VERB cana-3678 31 16 an an DET cana-3678 31 17 underlying underlie VERB cana-3678 31 18 asset asset NOUN cana-3678 31 19 at at ADP cana-3678 31 20 a a DET cana-3678 31 21 later later ADJ cana-3678 31 22 date date NOUN cana-3678 31 23 . . PUNCT cana-3678 32 1 these these DET cana-3678 32 2 instruments instrument NOUN cana-3678 32 3 , , PUNCT cana-3678 32 4 including include VERB cana-3678 32 5 options option NOUN cana-3678 32 6 , , PUNCT cana-3678 32 7 futures future NOUN cana-3678 32 8 , , PUNCT cana-3678 32 9 swaps swap NOUN cana-3678 32 10 and and CCONJ cana-3678 32 11 forwards forward NOUN cana-3678 32 12 , , PUNCT cana-3678 32 13 were be AUX cana-3678 32 14 utilized utilize VERB cana-3678 32 15 for for ADP cana-3678 32 16 speculation speculation NOUN cana-3678 32 17 and and CCONJ cana-3678 32 18 risk risk NOUN cana-3678 32 19 management management NOUN cana-3678 32 20 in in ADP cana-3678 32 21 an an DET cana-3678 32 22 investment investment NOUN cana-3678 32 23 . . PUNCT cana-3678 33 1 an an DET cana-3678 33 2 option option NOUN cana-3678 33 3 is be AUX cana-3678 33 4 a a DET cana-3678 33 5 financial financial ADJ cana-3678 33 6 agreement agreement NOUN cana-3678 33 7 that that PRON cana-3678 33 8 provides provide VERB cana-3678 33 9 option option NOUN cana-3678 33 10 holders holder NOUN cana-3678 33 11 the the DET cana-3678 33 12 privilege privilege NOUN cana-3678 33 13 to to PART cana-3678 33 14 purchase purchase VERB cana-3678 33 15 or or CCONJ cana-3678 33 16 sell sell VERB cana-3678 33 17 an an DET cana-3678 33 18 underlying underlying NOUN cana-3678 33 19 from from ADP cana-3678 33 20 option option NOUN cana-3678 33 21 writers writer NOUN cana-3678 33 22 at at ADP cana-3678 33 23 a a DET cana-3678 33 24 predetermined predetermined ADJ cana-3678 33 25 date date NOUN cana-3678 33 26 and and CCONJ cana-3678 33 27 price price NOUN cana-3678 33 28 . . PUNCT cana-3678 34 1 the the DET cana-3678 34 2 agreement agreement NOUN cana-3678 34 3 that that PRON cana-3678 34 4 grants grant VERB cana-3678 34 5 option option NOUN cana-3678 34 6 holders holder NOUN cana-3678 34 7 the the DET cana-3678 34 8 ability ability NOUN cana-3678 34 9 to to PART cana-3678 34 10 purchase purchase VERB cana-3678 34 11 an an DET cana-3678 34 12 underlying underlie VERB cana-3678 34 13 asset asset NOUN cana-3678 34 14 is be AUX cana-3678 34 15 referred refer VERB cana-3678 34 16 to to ADP cana-3678 34 17 as as ADP cana-3678 34 18 a a DET cana-3678 34 19 call call NOUN cana-3678 34 20 option option NOUN cana-3678 34 21 , , PUNCT cana-3678 34 22 whereas whereas SCONJ cana-3678 34 23 the the DET cana-3678 34 24 agreement agreement NOUN cana-3678 34 25 that that PRON cana-3678 34 26 allows allow VERB cana-3678 34 27 option option NOUN cana-3678 34 28 holders holder NOUN cana-3678 34 29 to to PART cana-3678 34 30 sell sell VERB cana-3678 34 31 an an DET cana-3678 34 32 underlying underlie VERB cana-3678 34 33 asset asset NOUN cana-3678 34 34 as as ADP cana-3678 34 35 a a DET cana-3678 34 36 put put NOUN cana-3678 34 37 option option NOUN cana-3678 34 38 . . PUNCT cana-3678 35 1 in in ADP cana-3678 35 2 1973 1973 NUM cana-3678 35 3 , , PUNCT cana-3678 35 4 fischer fischer PROPN cana-3678 35 5 black black PROPN cana-3678 35 6 and and CCONJ cana-3678 35 7 myron myron PROPN cana-3678 35 8 scholes schole VERB cana-3678 36 1 [ [ X cana-3678 36 2 1 1 X cana-3678 36 3 ] ] PUNCT cana-3678 36 4 constructed construct VERB cana-3678 36 5 the the DET cana-3678 36 6 black black ADJ cana-3678 36 7 - - PUNCT cana-3678 36 8 scholes schole NOUN cana-3678 36 9 model model NOUN cana-3678 36 10 for for ADP cana-3678 36 11 determining determine VERB cana-3678 36 12 prices price NOUN cana-3678 36 13 of of ADP cana-3678 36 14 options option NOUN cana-3678 36 15 . . PUNCT cana-3678 37 1 however however ADV cana-3678 37 2 , , PUNCT cana-3678 37 3 their their PRON cana-3678 37 4 model model NOUN cana-3678 37 5 required require VERB cana-3678 37 6 various various ADJ cana-3678 37 7 assumptions assumption NOUN cana-3678 37 8 such such ADJ cana-3678 37 9 as as ADP cana-3678 37 10 constant constant ADJ cana-3678 37 11 volatility volatility NOUN cana-3678 37 12 , , PUNCT cana-3678 37 13 no no DET cana-3678 37 14 transaction transaction NOUN cana-3678 37 15 costs cost NOUN cana-3678 37 16 and and CCONJ cana-3678 37 17 perfect perfect ADJ cana-3678 37 18 liquidity liquidity NOUN cana-3678 37 19 . . PUNCT cana-3678 38 1 but but CCONJ cana-3678 38 2 this this DET cana-3678 38 3 model model NOUN cana-3678 38 4 is be AUX cana-3678 38 5 not not PART cana-3678 38 6 best well ADV cana-3678 38 7 suited suit VERB cana-3678 38 8 for for ADP cana-3678 38 9 real real ADJ cana-3678 38 10 financial financial ADJ cana-3678 38 11 market market NOUN cana-3678 38 12 . . PUNCT cana-3678 39 1 in in ADP cana-3678 39 2 real real ADJ cana-3678 39 3 world world NOUN cana-3678 39 4 , , PUNCT cana-3678 39 5 options option NOUN cana-3678 39 6 are be AUX cana-3678 39 7 generally generally ADV cana-3678 39 8 illiquid illiquid ADJ cana-3678 39 9 . . PUNCT cana-3678 40 1 also also ADV cana-3678 40 2 underlying underlie VERB cana-3678 40 3 assets asset NOUN cana-3678 40 4 prices price NOUN cana-3678 40 5 change change VERB cana-3678 40 6 randomly randomly ADV cana-3678 40 7 with with ADP cana-3678 40 8 jump jump NOUN cana-3678 40 9 . . PUNCT cana-3678 41 1 therefore therefore ADV cana-3678 41 2 , , PUNCT cana-3678 41 3 many many ADJ cana-3678 41 4 researchers researcher NOUN cana-3678 41 5 tried try VERB cana-3678 41 6 to to PART cana-3678 41 7 develop develop VERB cana-3678 41 8 more more ADV cana-3678 41 9 realistic realistic ADJ cana-3678 41 10 model model NOUN cana-3678 41 11 of of ADP cana-3678 41 12 black black NOUN cana-3678 41 13 - - PUNCT cana-3678 41 14 scholes schole NOUN cana-3678 41 15 by by ADP cana-3678 41 16 changing change VERB cana-3678 41 17 some some DET cana-3678 41 18 assumptions assumption NOUN cana-3678 41 19 . . PUNCT cana-3678 42 1 transaction transaction NOUN cana-3678 42 2 cost cost NOUN cana-3678 42 3 is be AUX cana-3678 42 4 also also ADV cana-3678 42 5 considered consider VERB cana-3678 42 6 in in ADP cana-3678 42 7 actual actual ADJ cana-3678 42 8 market market NOUN cana-3678 42 9 . . PUNCT cana-3678 43 1 volatility volatility NOUN cana-3678 43 2 affects affect VERB cana-3678 43 3 the the DET cana-3678 43 4 option option NOUN cana-3678 43 5 prices price NOUN cana-3678 43 6 and and CCONJ cana-3678 43 7 its its PRON cana-3678 43 8 knowledge knowledge NOUN cana-3678 43 9 can can AUX cana-3678 43 10 help help VERB cana-3678 43 11 buffer buffer VERB cana-3678 43 12 against against ADP cana-3678 43 13 losses loss NOUN cana-3678 43 14 . . PUNCT cana-3678 44 1 the the DET cana-3678 44 2 black black ADJ cana-3678 44 3 - - PUNCT cana-3678 44 4 scholes schole NOUN cana-3678 44 5 model model NOUN cana-3678 44 6 is be AUX cana-3678 44 7 updated update VERB cana-3678 44 8 by by ADP cana-3678 44 9 considering consider VERB cana-3678 44 10 transaction transaction NOUN cana-3678 44 11 cost cost NOUN cana-3678 44 12 and and CCONJ cana-3678 44 13 volatility volatility NOUN cana-3678 44 14 ( ( PUNCT cana-3678 44 15 see,[2],[3],[4],[5],[6],[7 see,[2],[3],[4],[5],[6],[7 NOUN cana-3678 44 16 ] ] PUNCT cana-3678 44 17 ) ) PUNCT cana-3678 44 18 . . PUNCT cana-3678 45 1 illiquid illiquid NOUN cana-3678 45 2 describes describe VERB cana-3678 45 3 the the DET cana-3678 45 4 condition condition NOUN cana-3678 45 5 of of ADP cana-3678 45 6 a a DET cana-3678 45 7 stock stock NOUN cana-3678 45 8 , , PUNCT cana-3678 45 9 bond bond NOUN cana-3678 45 10 , , PUNCT cana-3678 45 11 or or CCONJ cana-3678 45 12 other other ADJ cana-3678 45 13 assets asset NOUN cana-3678 45 14 that that PRON cana-3678 45 15 can can AUX cana-3678 45 16 not not PART cana-3678 45 17 be be AUX cana-3678 45 18 quickly quickly ADV cana-3678 45 19 or or CCONJ cana-3678 45 20 easily easily ADV cana-3678 45 21 sold sell VERB cana-3678 45 22 or or CCONJ cana-3678 45 23 converted convert VERB cana-3678 45 24 to to ADP cana-3678 45 25 cash cash NOUN cana-3678 45 26 without without ADP cana-3678 45 27 incurring incur VERB cana-3678 45 28 a a DET cana-3678 45 29 significant significant ADJ cana-3678 45 30 loss loss NOUN cana-3678 45 31 in in ADP cana-3678 45 32 value value NOUN cana-3678 45 33 . . PUNCT cana-3678 46 1 illiquid illiquid ADJ cana-3678 46 2 assets asset NOUN cana-3678 46 3 can can AUX cana-3678 46 4 be be AUX cana-3678 46 5 challenging challenge VERB cana-3678 46 6 to to PART cana-3678 46 7 sell sell VERB cana-3678 46 8 promptly promptly ADV cana-3678 46 9 due due ADJ cana-3678 46 10 to to ADP cana-3678 46 11 minimal minimal ADJ cana-3678 46 12 trading trading NOUN cana-3678 46 13 activity activity NOUN cana-3678 46 14 or or CCONJ cana-3678 46 15 interest interest NOUN cana-3678 46 16 in in ADP cana-3678 46 17 the the DET cana-3678 46 18 matter matter NOUN cana-3678 46 19 , , PUNCT cana-3678 46 20 signified signify VERB cana-3678 46 21 by by ADP cana-3678 46 22 an an DET cana-3678 46 23 absence absence NOUN cana-3678 46 24 of of ADP cana-3678 46 25 eager eager ADJ cana-3678 46 26 and and CCONJ cana-3678 46 27 willing willing ADJ cana-3678 46 28 investors investor NOUN cana-3678 46 29 or or CCONJ cana-3678 46 30 speculators speculator NOUN cana-3678 46 31 looking look VERB cana-3678 46 32 to to PART cana-3678 46 33 buy buy VERB cana-3678 46 34 or or CCONJ cana-3678 46 35 sell sell VERB cana-3678 46 36 the the DET cana-3678 46 37 asset asset NOUN cana-3678 46 38 . . PUNCT cana-3678 47 1 consequently consequently ADV cana-3678 47 2 , , PUNCT cana-3678 47 3 illiquid illiquid ADJ cana-3678 47 4 assets asset NOUN cana-3678 47 5 usually usually ADV cana-3678 47 6 exhibit exhibit VERB cana-3678 47 7 reduced reduced ADJ cana-3678 47 8 trading trading NOUN cana-3678 47 9 volume volume NOUN cana-3678 47 10 , , PUNCT cana-3678 47 11 broader broad ADJ cana-3678 47 12 bid bid NOUN cana-3678 47 13 - - PUNCT cana-3678 47 14 ask ask NOUN cana-3678 47 15 spreads spread NOUN cana-3678 47 16 , , PUNCT cana-3678 47 17 and and CCONJ cana-3678 47 18 heightened heighten VERB cana-3678 47 19 price price NOUN cana-3678 47 20 volatility volatility NOUN cana-3678 47 21 . . PUNCT cana-3678 48 1 in in ADP cana-3678 48 2 2005 2005 NUM cana-3678 48 3 , , PUNCT cana-3678 48 4 generalised generalised ADJ cana-3678 48 5 model model NOUN cana-3678 48 6 of of ADP cana-3678 48 7 black black NOUN cana-3678 48 8 - - PUNCT cana-3678 48 9 scholes schole NOUN cana-3678 48 10 in in ADP cana-3678 48 11 illiquid illiquid ADJ cana-3678 48 12 market market NOUN cana-3678 48 13 was be AUX cana-3678 48 14 derived derive VERB cana-3678 48 15 . . PUNCT cana-3678 49 1 ( ( PUNCT cana-3678 49 2 [ [ X cana-3678 49 3 8 8 NUM cana-3678 49 4 ] ] NUM cana-3678 49 5 ) ) PUNCT cana-3678 49 6 . . PUNCT cana-3678 50 1 presence presence NOUN cana-3678 50 2 of of ADP cana-3678 50 3 price price NOUN cana-3678 50 4 impact impact NOUN cana-3678 50 5 has have AUX cana-3678 50 6 been be AUX cana-3678 50 7 also also ADV cana-3678 50 8 studied study VERB cana-3678 50 9 by by ADP cana-3678 50 10 researchers researcher NOUN cana-3678 50 11 ( ( PUNCT cana-3678 50 12 [ [ X cana-3678 50 13 9],[10 9],[10 NUM cana-3678 50 14 ] ] PUNCT cana-3678 50 15 ) ) PUNCT cana-3678 50 16 . . PUNCT cana-3678 51 1 in in ADP cana-3678 51 2 2013 2013 NUM cana-3678 51 3 , , PUNCT cana-3678 51 4 model model NOUN cana-3678 51 5 ( ( PUNCT cana-3678 51 6 [ [ X cana-3678 51 7 8 8 NUM cana-3678 51 8 ] ] PUNCT cana-3678 51 9 ) ) PUNCT cana-3678 51 10 was be AUX cana-3678 51 11 revised revise VERB cana-3678 51 12 and and CCONJ cana-3678 51 13 add add VERB cana-3678 51 14 illiquidity illiquidity NOUN cana-3678 51 15 with with ADP cana-3678 51 16 jump jump NOUN cana-3678 51 17 ( ( PUNCT cana-3678 51 18 [ [ X cana-3678 51 19 11 11 NUM cana-3678 51 20 ] ] NUM cana-3678 51 21 ) ) PUNCT cana-3678 51 22 . . PUNCT cana-3678 52 1 in in ADP cana-3678 52 2 2016 2016 NUM cana-3678 52 3 , , PUNCT cana-3678 52 4 illiquid illiquid ADJ cana-3678 52 5 market market NOUN cana-3678 52 6 with with ADP cana-3678 52 7 transaction transaction NOUN cana-3678 52 8 cost cost NOUN cana-3678 52 9 model model NOUN cana-3678 52 10 was be AUX cana-3678 52 11 derived derive VERB cana-3678 52 12 ( ( PUNCT cana-3678 52 13 [ [ X cana-3678 52 14 12 12 NUM cana-3678 52 15 ] ] PUNCT cana-3678 52 16 ) ) PUNCT cana-3678 52 17 . . PUNCT cana-3678 53 1 in in ADP cana-3678 53 2 2021 2021 NUM cana-3678 53 3 , , PUNCT cana-3678 53 4 the the DET cana-3678 53 5 idea idea NOUN cana-3678 53 6 of of ADP cana-3678 53 7 ( ( PUNCT cana-3678 53 8 [ [ X cana-3678 53 9 11 11 NUM cana-3678 53 10 ] ] PUNCT cana-3678 53 11 and and CCONJ cana-3678 53 12 [ [ X cana-3678 53 13 12 12 NUM cana-3678 53 14 ] ] PUNCT cana-3678 53 15 ) ) PUNCT cana-3678 53 16 was be AUX cana-3678 53 17 combined combine VERB cana-3678 53 18 and and CCONJ cana-3678 53 19 black black ADJ cana-3678 53 20 - - PUNCT cana-3678 53 21 scholes schole NOUN cana-3678 53 22 model model NOUN cana-3678 53 23 with with ADP cana-3678 53 24 transaction transaction NOUN cana-3678 53 25 cost cost NOUN cana-3678 53 26 with with ADP cana-3678 53 27 jumps jump NOUN cana-3678 53 28 in in ADP cana-3678 53 29 illiquid illiquid ADJ cana-3678 53 30 market market NOUN cana-3678 53 31 was be AUX cana-3678 53 32 derived derive VERB cana-3678 53 33 ( ( PUNCT cana-3678 53 34 [ [ X cana-3678 53 35 13 13 NUM cana-3678 53 36 ] ] NUM cana-3678 53 37 ) ) PUNCT cana-3678 53 38 . . PUNCT cana-3678 54 1 the the DET cana-3678 54 2 model model NOUN cana-3678 54 3 derived derive VERB cana-3678 54 4 in in ADP cana-3678 54 5 ( ( PUNCT cana-3678 54 6 [ [ X cana-3678 54 7 13 13 NUM cana-3678 54 8 ] ] PUNCT cana-3678 54 9 ) ) PUNCT cana-3678 54 10 is be AUX cana-3678 54 11 nonlinear nonlinear ADJ cana-3678 54 12 and and CCONJ cana-3678 54 13 more more ADV cana-3678 54 14 realistic realistic ADJ cana-3678 54 15 to to ADP cana-3678 54 16 the the DET cana-3678 54 17 real real ADJ cana-3678 54 18 financial financial ADJ cana-3678 54 19 market market NOUN cana-3678 54 20 . . PUNCT cana-3678 55 1 differential differential ADJ cana-3678 55 2 equations equation NOUN cana-3678 55 3 have have AUX cana-3678 55 4 been be AUX cana-3678 55 5 solved solve VERB cana-3678 55 6 using use VERB cana-3678 55 7 numerical numerical ADJ cana-3678 55 8 methods method NOUN cana-3678 55 9 . . PUNCT cana-3678 56 1 optimization optimization NOUN cana-3678 56 2 methods method NOUN cana-3678 56 3 like like ADP cana-3678 56 4 least least ADJ cana-3678 56 5 squares square NOUN cana-3678 56 6 finite finite PROPN cana-3678 56 7 element element NOUN cana-3678 56 8 methods method NOUN cana-3678 56 9 [ [ X cana-3678 56 10 14],[15 14],[15 NUM cana-3678 56 11 ] ] X cana-3678 56 12 ) ) PUNCT cana-3678 56 13 , , PUNCT cana-3678 56 14 and and CCONJ cana-3678 56 15 element element NOUN cana-3678 56 16 free free ADJ cana-3678 56 17 galerkin galerkin ADJ cana-3678 56 18 methods method NOUN cana-3678 56 19 [ [ X cana-3678 56 20 16 16 NUM cana-3678 56 21 ] ] PUNCT cana-3678 56 22 have have AUX cana-3678 56 23 been be AUX cana-3678 56 24 used use VERB cana-3678 56 25 . . PUNCT cana-3678 57 1 these these DET cana-3678 57 2 methods method NOUN cana-3678 57 3 are be AUX cana-3678 57 4 based base VERB cana-3678 57 5 on on ADP cana-3678 57 6 mesh mesh NOUN cana-3678 57 7 - - PUNCT cana-3678 57 8 free free ADJ cana-3678 57 9 formulations formulation NOUN cana-3678 57 10 . . PUNCT cana-3678 58 1 theoretical theoretical ADJ cana-3678 58 2 convergence convergence NOUN cana-3678 58 3 criteria criterion NOUN cana-3678 58 4 for for ADP cana-3678 58 5 both both CCONJ cana-3678 58 6 the the DET cana-3678 58 7 methods method NOUN cana-3678 58 8 have have AUX cana-3678 58 9 been be AUX cana-3678 58 10 examined examine VERB cana-3678 58 11 [ [ X cana-3678 58 12 17 17 NUM cana-3678 58 13 ] ] PUNCT cana-3678 58 14 . . PUNCT cana-3678 59 1 these these DET cana-3678 59 2 concepts concept NOUN cana-3678 59 3 were be AUX cana-3678 59 4 applied apply VERB cana-3678 59 5 to to ADP cana-3678 59 6 neural neural ADJ cana-3678 59 7 networks network NOUN cana-3678 59 8 in in ADP cana-3678 59 9 [ [ X cana-3678 59 10 18 18 NUM cana-3678 59 11 ] ] PUNCT cana-3678 59 12 , , PUNCT cana-3678 59 13 though though SCONJ cana-3678 59 14 using use VERB cana-3678 59 15 neural neural ADJ cana-3678 59 16 networks network NOUN cana-3678 59 17 in in ADP cana-3678 59 18 this this DET cana-3678 59 19 context context NOUN cana-3678 59 20 has have AUX cana-3678 59 21 recently recently ADV cana-3678 59 22 experienced experience VERB cana-3678 59 23 a a DET cana-3678 59 24 resurgence resurgence NOUN cana-3678 59 25 of of ADP cana-3678 59 26 interest interest NOUN cana-3678 59 27 as as SCONJ cana-3678 59 28 seen see VERB cana-3678 59 29 in in ADP cana-3678 59 30 ( ( PUNCT cana-3678 59 31 [ [ X cana-3678 59 32 18],[19],[20],[21],[22],[23 18],[19],[20],[21],[22],[23 NOUN cana-3678 59 33 ] ] PUNCT cana-3678 59 34 ) ) PUNCT cana-3678 59 35 . . PUNCT cana-3678 60 1 these these DET cana-3678 60 2 recent recent ADJ cana-3678 60 3 works work NOUN cana-3678 60 4 have have AUX cana-3678 60 5 shown show VERB cana-3678 60 6 that that SCONJ cana-3678 60 7 remarkably remarkably ADV cana-3678 60 8 simple simple ADJ cana-3678 60 9 communications communication NOUN cana-3678 60 10 on on ADP cana-3678 60 11 applied apply VERB cana-3678 60 12 nonlinear nonlinear ADJ cana-3678 60 13 analysis analysis NOUN cana-3678 60 14 issn issn NOUN cana-3678 60 15 : : PUNCT cana-3678 60 16 1074 1074 NUM cana-3678 60 17 - - PUNCT cana-3678 60 18 133x 133x NUM cana-3678 60 19 vol vol NOUN cana-3678 60 20 32 32 NUM cana-3678 60 21 no no NOUN cana-3678 60 22 . . PUNCT cana-3678 61 1 8s 8s PROPN cana-3678 61 2 ( ( PUNCT cana-3678 61 3 2025 2025 NUM cana-3678 61 4 ) ) PUNCT cana-3678 61 5 322 322 NUM cana-3678 61 6 https://internationalpubls.com https://internationalpubls.com X cana-3678 61 7 implementations implementation NOUN cana-3678 61 8 of of ADP cana-3678 61 9 deep deep ADJ cana-3678 61 10 neural neural ADJ cana-3678 61 11 networks network NOUN cana-3678 61 12 can can AUX cana-3678 61 13 be be AUX cana-3678 61 14 used use VERB cana-3678 61 15 to to PART cana-3678 61 16 solve solve VERB cana-3678 61 17 relatively relatively ADV cana-3678 61 18 broad broad ADJ cana-3678 61 19 classes class NOUN cana-3678 61 20 of of ADP cana-3678 61 21 differential differential ADJ cana-3678 61 22 equations equation NOUN cana-3678 61 23 . . PUNCT cana-3678 62 1 in in ADP cana-3678 62 2 this this DET cana-3678 62 3 paper paper NOUN cana-3678 62 4 , , PUNCT cana-3678 62 5 from from ADP cana-3678 62 6 the the DET cana-3678 62 7 extended extended ADJ cana-3678 62 8 model model NOUN cana-3678 62 9 of of ADP cana-3678 62 10 ( ( PUNCT cana-3678 62 11 [ [ X cana-3678 62 12 13 13 NUM cana-3678 62 13 ] ] NUM cana-3678 62 14 ) ) PUNCT cana-3678 62 15 , , PUNCT cana-3678 62 16 transaction transaction NOUN cana-3678 62 17 cost cost NOUN cana-3678 62 18 model model NOUN cana-3678 62 19 with with ADP cana-3678 62 20 illiquidity illiquidity NOUN cana-3678 62 21 is be AUX cana-3678 62 22 used use VERB cana-3678 62 23 . . PUNCT cana-3678 63 1 according accord VERB cana-3678 63 2 to to ADP cana-3678 63 3 ( ( PUNCT cana-3678 63 4 [ [ X cana-3678 63 5 24 24 NUM cana-3678 63 6 ] ] NUM cana-3678 63 7 ) ) PUNCT cana-3678 63 8 , , PUNCT cana-3678 63 9 nonlinear nonlinear ADJ cana-3678 63 10 model model NOUN cana-3678 63 11 was be AUX cana-3678 63 12 converted convert VERB cana-3678 63 13 into into ADP cana-3678 63 14 nonlinear nonlinear ADJ cana-3678 63 15 ordinary ordinary ADJ cana-3678 63 16 differential differential ADJ cana-3678 63 17 equation equation NOUN cana-3678 63 18 using use VERB cana-3678 63 19 semi semi ADJ cana-3678 63 20 discretization discretization NOUN cana-3678 63 21 technique technique NOUN cana-3678 63 22 . . PUNCT cana-3678 64 1 the the DET cana-3678 64 2 converted converted ADJ cana-3678 64 3 nonlinear nonlinear ADJ cana-3678 64 4 ordinary ordinary ADJ cana-3678 64 5 differential differential ADJ cana-3678 64 6 equation equation NOUN cana-3678 64 7 was be AUX cana-3678 64 8 solved solve VERB cana-3678 64 9 using use VERB cana-3678 64 10 the the DET cana-3678 64 11 fourth fourth ADJ cana-3678 64 12 order order NOUN cana-3678 64 13 runge runge NOUN cana-3678 64 14 - - PUNCT cana-3678 64 15 kuttafehlberg kuttafehlberg NOUN cana-3678 64 16 integration integration NOUN cana-3678 64 17 technique technique NOUN cana-3678 64 18 . . PUNCT cana-3678 65 1 in in ADP cana-3678 65 2 this this DET cana-3678 65 3 method method NOUN cana-3678 65 4 both both CCONJ cana-3678 65 5 the the DET cana-3678 65 6 variables variable NOUN cana-3678 65 7 transaction transaction NOUN cana-3678 65 8 costs cost NOUN cana-3678 65 9 and and CCONJ cana-3678 65 10 liquidity liquidity NOUN cana-3678 65 11 parameter parameter NOUN cana-3678 65 12 were be AUX cana-3678 65 13 taken take VERB cana-3678 65 14 in in ADP cana-3678 65 15 a a DET cana-3678 65 16 range range NOUN cana-3678 65 17 from from ADP cana-3678 65 18 0 0 NUM cana-3678 65 19 to to ADP cana-3678 65 20 0.03 0.03 NUM cana-3678 65 21 . . PUNCT cana-3678 66 1 one one NUM cana-3678 66 2 variable variable NOUN cana-3678 66 3 keeping keep VERB cana-3678 66 4 fix fix NOUN cana-3678 66 5 and and CCONJ cana-3678 66 6 other other ADJ cana-3678 66 7 is be AUX cana-3678 66 8 vary vary ADJ cana-3678 66 9 in in ADP cana-3678 66 10 a a DET cana-3678 66 11 given give VERB cana-3678 66 12 range range NOUN cana-3678 66 13 . . PUNCT cana-3678 67 1 so so ADV cana-3678 67 2 eventually eventually ADV cana-3678 67 3 both both PRON cana-3678 67 4 are be AUX cana-3678 67 5 treated treat VERB cana-3678 67 6 as as ADP cana-3678 67 7 constants constant NOUN cana-3678 67 8 . . PUNCT cana-3678 68 1 in in ADP cana-3678 68 2 this this DET cana-3678 68 3 paper paper NOUN cana-3678 68 4 both both DET cana-3678 68 5 transaction transaction NOUN cana-3678 68 6 costs cost NOUN cana-3678 68 7 and and CCONJ cana-3678 68 8 liquidity liquidity NOUN cana-3678 68 9 parameter parameter NOUN cana-3678 68 10 are be AUX cana-3678 68 11 considered consider VERB cana-3678 68 12 as as ADP cana-3678 68 13 variables variable NOUN cana-3678 68 14 . . PUNCT cana-3678 69 1 transaction transaction NOUN cana-3678 69 2 costs cost NOUN cana-3678 69 3 is be AUX cana-3678 69 4 defined define VERB cana-3678 69 5 in in ADP cana-3678 69 6 a a DET cana-3678 69 7 function function NOUN cana-3678 69 8 form form NOUN cana-3678 69 9 and and CCONJ cana-3678 69 10 liquidity liquidity NOUN cana-3678 69 11 parameter parameter NOUN cana-3678 69 12 randomly randomly ADV cana-3678 69 13 vary vary VERB cana-3678 69 14 in in ADP cana-3678 69 15 a a DET cana-3678 69 16 range range NOUN cana-3678 69 17 from from ADP cana-3678 69 18 0 0 NUM cana-3678 69 19 to to ADP cana-3678 69 20 0.03 0.03 NUM cana-3678 69 21 . . PUNCT cana-3678 70 1 so so ADV cana-3678 70 2 , , PUNCT cana-3678 70 3 the the DET cana-3678 70 4 proposed propose VERB cana-3678 70 5 model model NOUN cana-3678 70 6 is be AUX cana-3678 70 7 completely completely ADV cana-3678 70 8 nonlinear nonlinear ADJ cana-3678 70 9 . . PUNCT cana-3678 71 1 the the DET cana-3678 71 2 converted converted ADJ cana-3678 71 3 nonlinear nonlinear ADJ cana-3678 71 4 ordinary ordinary ADJ cana-3678 71 5 differential differential ADJ cana-3678 71 6 equation equation NOUN cana-3678 71 7 is be AUX cana-3678 71 8 solved solve VERB cana-3678 71 9 using use VERB cana-3678 71 10 deep deep ADJ cana-3678 71 11 learning learning NOUN cana-3678 71 12 based base VERB cana-3678 71 13 fully fully ADV cana-3678 71 14 connected connect VERB cana-3678 71 15 neural neural ADJ cana-3678 71 16 network network NOUN cana-3678 71 17 . . PUNCT cana-3678 72 1 experimental experimental ADJ cana-3678 72 2 results result NOUN cana-3678 72 3 are be AUX cana-3678 72 4 used use VERB cana-3678 72 5 to to PART cana-3678 72 6 check check VERB cana-3678 72 7 accuracy accuracy NOUN cana-3678 72 8 of of ADP cana-3678 72 9 the the DET cana-3678 72 10 proposed propose VERB cana-3678 72 11 method method NOUN cana-3678 72 12 . . PUNCT cana-3678 73 1 2 2 X cana-3678 73 2 . . X cana-3678 73 3 objectives objective VERB cana-3678 73 4 two two NUM cana-3678 73 5 types type NOUN cana-3678 73 6 of of ADP cana-3678 73 7 assets asset NOUN cana-3678 73 8 are be AUX cana-3678 73 9 generally generally ADV cana-3678 73 10 traded trade VERB cana-3678 73 11 in in ADP cana-3678 73 12 a a DET cana-3678 73 13 real real ADJ cana-3678 73 14 financial financial ADJ cana-3678 73 15 market market NOUN cana-3678 73 16 . . PUNCT cana-3678 74 1 one one NUM cana-3678 74 2 is be AUX cana-3678 74 3 a a DET cana-3678 74 4 risk risk NOUN cana-3678 74 5 - - PUNCT cana-3678 74 6 free free ADJ cana-3678 74 7 asset asset NOUN cana-3678 74 8 and and CCONJ cana-3678 74 9 second second ADJ cana-3678 74 10 is be AUX cana-3678 74 11 risky risky ADJ cana-3678 74 12 asset asset NOUN cana-3678 74 13 . . PUNCT cana-3678 75 1 let let VERB cana-3678 75 2 at at PART cana-3678 75 3 denote denote VERB cana-3678 75 4 the the DET cana-3678 75 5 risk risk NOUN cana-3678 75 6 - - PUNCT cana-3678 75 7 free free ADJ cana-3678 75 8 asset asset NOUN cana-3678 75 9 price price NOUN cana-3678 75 10 and and CCONJ cana-3678 75 11 st st PROPN cana-3678 75 12 denote denote VERB cana-3678 75 13 the the DET cana-3678 75 14 risky risky ADJ cana-3678 75 15 asset asset NOUN cana-3678 75 16 prices price NOUN cana-3678 75 17 at at ADP cana-3678 75 18 time time NOUN cana-3678 75 19 t t PROPN cana-3678 75 20 where where SCONJ cana-3678 75 21 t t PROPN cana-3678 75 22 > > X cana-3678 75 23 0 0 X cana-3678 75 24 . . PUNCT cana-3678 76 1 let let VERB cana-3678 76 2 t t NOUN cana-3678 76 3 be be AUX cana-3678 76 4 the the DET cana-3678 76 5 time time NOUN cana-3678 76 6 of of ADP cana-3678 76 7 maturity maturity NOUN cana-3678 76 8 , , PUNCT cana-3678 76 9 k k X cana-3678 76 10 be be VERB cana-3678 76 11 the the DET cana-3678 76 12 striking strike VERB cana-3678 76 13 price price NOUN cana-3678 76 14 and and CCONJ cana-3678 77 1 β„Ž(𝑆𝑇 β„Ž(𝑆𝑇 PROPN cana-3678 77 2 ) ) PUNCT cana-3678 77 3 = = PUNCT cana-3678 77 4 π‘šπ‘Žπ‘₯{𝑆𝑇 π‘šπ‘Žπ‘₯{𝑆𝑇 PROPN cana-3678 78 1 βˆ’ βˆ’ PROPN cana-3678 78 2 𝐾 𝐾 PROPN cana-3678 78 3 , , PUNCT cana-3678 78 4 0 0 NUM cana-3678 78 5 } } PUNCT cana-3678 78 6 be be AUX cana-3678 78 7 the the DET cana-3678 78 8 payoff payoff NOUN cana-3678 78 9 at at ADP cana-3678 78 10 time time NOUN cana-3678 78 11 t t PROPN cana-3678 78 12 that that PRON cana-3678 78 13 is be AUX cana-3678 78 14 at at ADP cana-3678 78 15 time time NOUN cana-3678 78 16 of of ADP cana-3678 78 17 maturity maturity NOUN cana-3678 78 18 of of ADP cana-3678 78 19 the the DET cana-3678 78 20 option option NOUN cana-3678 78 21 . . PUNCT cana-3678 79 1 in in ADP cana-3678 79 2 1973 1973 NUM cana-3678 79 3 , , PUNCT cana-3678 79 4 fischer fischer PROPN cana-3678 79 5 black black PROPN cana-3678 79 6 and and CCONJ cana-3678 79 7 myron myron PROPN cana-3678 79 8 scholes schole VERB cana-3678 80 1 [ [ X cana-3678 80 2 1 1 X cana-3678 80 3 ] ] PUNCT cana-3678 80 4 derived derive VERB cana-3678 80 5 the the DET cana-3678 80 6 linear linear ADJ cana-3678 80 7 black black ADJ cana-3678 80 8 - - PUNCT cana-3678 80 9 scholes schole NOUN cana-3678 80 10 model model NOUN cana-3678 80 11 for for ADP cana-3678 80 12 option option NOUN cana-3678 80 13 pricing pricing NOUN cana-3678 80 14 . . PUNCT cana-3678 81 1 according accord VERB cana-3678 81 2 to to ADP cana-3678 81 3 this this DET cana-3678 81 4 model model NOUN cana-3678 81 5 the the DET cana-3678 81 6 risk risk NOUN cana-3678 81 7 - - PUNCT cana-3678 81 8 free free ADJ cana-3678 81 9 asset asset NOUN cana-3678 81 10 price price NOUN cana-3678 81 11 at at ADP cana-3678 81 12 follows follow VERB cana-3678 81 13 𝑑𝐴𝑑 𝑑𝐴𝑑 NOUN cana-3678 81 14 = = PROPN cana-3678 81 15 π‘Ÿπ΄π‘‘π‘‘π‘‘ π‘Ÿπ΄π‘‘π‘‘π‘‘ PROPN cana-3678 81 16 ( ( PUNCT cana-3678 81 17 1 1 NUM cana-3678 81 18 ) ) PUNCT cana-3678 81 19 where where SCONJ cana-3678 81 20 r r NOUN cana-3678 81 21 is be AUX cana-3678 81 22 the the DET cana-3678 81 23 risk risk NOUN cana-3678 81 24 - - PUNCT cana-3678 81 25 free free ADJ cana-3678 81 26 interest interest NOUN cana-3678 81 27 rate rate NOUN cana-3678 81 28 . . PUNCT cana-3678 82 1 also also ADV cana-3678 82 2 , , PUNCT cana-3678 82 3 the the DET cana-3678 82 4 price price NOUN cana-3678 82 5 of of ADP cana-3678 82 6 risky risky ADJ cana-3678 82 7 asset asset NOUN cana-3678 82 8 𝑆𝑑 𝑆𝑑 PROPN cana-3678 82 9 satisfies satisfy VERB cana-3678 82 10 𝑑𝑆𝑑 𝑑𝑆𝑑 ADJ cana-3678 82 11 = = PUNCT cana-3678 82 12 𝑆𝑑(πœ‡π‘‘π‘‘ 𝑆𝑑(πœ‡π‘‘π‘‘ NOUN cana-3678 82 13 + + CCONJ cana-3678 82 14 πœŽπ‘‘π‘Šπ‘‘ πœŽπ‘‘π‘Šπ‘‘ NOUN cana-3678 82 15 ) ) PUNCT cana-3678 82 16 ( ( PUNCT cana-3678 82 17 2 2 X cana-3678 82 18 ) ) PUNCT cana-3678 82 19 where where SCONJ cana-3678 82 20 Β΅ Β΅ NOUN cana-3678 82 21 is be AUX cana-3678 82 22 the the DET cana-3678 82 23 constant constant ADJ cana-3678 82 24 drift drift NOUN cana-3678 82 25 and and CCONJ cana-3678 82 26 Οƒ Οƒ PROPN cana-3678 82 27 is be AUX cana-3678 82 28 the the DET cana-3678 82 29 constant constant ADJ cana-3678 82 30 volatility volatility NOUN cana-3678 82 31 , , PUNCT cana-3678 82 32 wt wt PROPN cana-3678 82 33 is be AUX cana-3678 82 34 a a DET cana-3678 82 35 standard standard ADJ cana-3678 82 36 one one NUM cana-3678 82 37 - - PUNCT cana-3678 82 38 dimensional dimensional ADJ cana-3678 82 39 brownian brownian ADJ cana-3678 82 40 motion motion NOUN cana-3678 82 41 . . PUNCT cana-3678 83 1 according accord VERB cana-3678 83 2 to to ADP cana-3678 83 3 ( ( PUNCT cana-3678 83 4 [ [ X cana-3678 83 5 13 13 NUM cana-3678 83 6 ] ] NUM cana-3678 83 7 ) ) PUNCT cana-3678 83 8 , , PUNCT cana-3678 83 9 for for ADP cana-3678 83 10 transaction transaction NOUN cana-3678 83 11 cost cost NOUN cana-3678 83 12 with with ADP cana-3678 83 13 jumps jump NOUN cana-3678 83 14 in in ADP cana-3678 83 15 illiquid illiquid ADJ cana-3678 83 16 market market NOUN cana-3678 83 17 , , PUNCT cana-3678 83 18 the the DET cana-3678 83 19 price price NOUN cana-3678 83 20 of of ADP cana-3678 83 21 the the DET cana-3678 83 22 risky risky ADJ cana-3678 83 23 asset asset NOUN cana-3678 83 24 is be AUX cana-3678 83 25 generated generate VERB cana-3678 83 26 by by ADP cana-3678 83 27 the the DET cana-3678 83 28 following follow VERB cana-3678 83 29 stochastic stochastic ADJ cana-3678 83 30 differential differential ADJ cana-3678 83 31 equation equation NOUN cana-3678 83 32 : : PUNCT cana-3678 83 33 𝑑𝑆𝑑 𝑑𝑆𝑑 X cana-3678 83 34 = = SYM cana-3678 83 35 𝑆𝑑(πœ‡(𝑑 𝑆𝑑(πœ‡(𝑑 PROPN cana-3678 83 36 , , PUNCT cana-3678 83 37 𝑆𝑑)𝑑𝑑 𝑆𝑑)𝑑𝑑 NOUN cana-3678 83 38 + + X cana-3678 83 39 𝜎(𝑑 𝜎(𝑑 NUM cana-3678 83 40 , , PUNCT cana-3678 83 41 𝑆𝑑)(π‘‘π‘Šπ‘‘ 𝑆𝑑)(π‘‘π‘Šπ‘‘ NOUN cana-3678 83 42 + + X cana-3678 83 43 π‘Žπ‘‘π‘€π‘‘ π‘Žπ‘‘π‘€π‘‘ NOUN cana-3678 83 44 ) ) PUNCT cana-3678 83 45 + + CCONJ cana-3678 84 1 πœ†(𝑑 πœ†(𝑑 PROPN cana-3678 84 2 , , PUNCT cana-3678 84 3 𝑆𝑑)π‘‘πœƒπ‘‘ 𝑆𝑑)π‘‘πœƒπ‘‘ VERB cana-3678 85 1 + + CCONJ cana-3678 85 2 π‘˜(𝑑 π‘˜(𝑑 NOUN cana-3678 85 3 , , PUNCT cana-3678 85 4 𝑆𝑑)π‘‘πœƒπ‘‘ 𝑆𝑑)π‘‘πœƒπ‘‘ X cana-3678 85 5 ) ) PUNCT cana-3678 85 6 ( ( PUNCT cana-3678 85 7 3 3 X cana-3678 85 8 ) ) PUNCT cana-3678 85 9 and and CCONJ cana-3678 85 10 πœƒπ‘‘ πœƒπ‘‘ ADV cana-3678 85 11 satisfies satisfy VERB cana-3678 85 12 π‘‘πœƒπ‘‘ π‘‘πœƒπ‘‘ NUM cana-3678 85 13 = = PUNCT cana-3678 85 14 πœ‚π‘‘π‘‘π‘‘ πœ‚π‘‘π‘‘π‘‘ NOUN cana-3678 85 15 + + X cana-3678 85 16 πœπ‘‘(π‘‘π‘Šπ‘‘ πœπ‘‘(π‘‘π‘Šπ‘‘ PROPN cana-3678 85 17 + + CCONJ cana-3678 85 18 𝑏𝑑𝑀𝑑 𝑏𝑑𝑀𝑑 NOUN cana-3678 85 19 ) ) PUNCT cana-3678 85 20 ( ( PUNCT cana-3678 85 21 4 4 X cana-3678 85 22 ) ) PUNCT cana-3678 85 23 where where SCONJ cana-3678 85 24 π‘Ÿ(𝑑 π‘Ÿ(𝑑 NOUN cana-3678 85 25 , , PUNCT cana-3678 85 26 𝑆𝑑 𝑆𝑑 PROPN cana-3678 85 27 ) ) PUNCT cana-3678 85 28 is be AUX cana-3678 85 29 the the DET cana-3678 85 30 interest interest NOUN cana-3678 85 31 rate rate NOUN cana-3678 85 32 , , PUNCT cana-3678 85 33 πœ‡(𝑑,𝑆𝑑 πœ‡(𝑑,𝑆𝑑 PROPN cana-3678 85 34 ) ) PUNCT cana-3678 85 35 is be AUX cana-3678 85 36 the the DET cana-3678 85 37 drift drift NOUN cana-3678 85 38 , , PUNCT cana-3678 85 39 𝜎(𝑑 𝜎(𝑑 PROPN cana-3678 85 40 , , PUNCT cana-3678 85 41 𝑆𝑑 𝑆𝑑 PROPN cana-3678 85 42 ) ) PUNCT cana-3678 85 43 is be AUX cana-3678 85 44 the the DET cana-3678 85 45 volatility volatility NOUN cana-3678 85 46 , , PUNCT cana-3678 85 47 a a PRON cana-3678 85 48 and and CCONJ cana-3678 85 49 b b NOUN cana-3678 85 50 are be AUX cana-3678 85 51 real real ADJ cana-3678 85 52 constants constant NOUN cana-3678 85 53 , , PUNCT cana-3678 85 54 π‘˜(𝑑 π‘˜(𝑑 PROPN cana-3678 85 55 , , PUNCT cana-3678 85 56 𝑆𝑑 𝑆𝑑 PROPN cana-3678 85 57 ) ) PUNCT cana-3678 85 58 is be AUX cana-3678 85 59 the the DET cana-3678 85 60 transaction transaction NOUN cana-3678 85 61 costs cost NOUN cana-3678 85 62 , , PUNCT cana-3678 86 1 𝑀𝑑 𝑀𝑑 PROPN cana-3678 86 2 = = PUNCT cana-3678 86 3 𝑁𝑑 𝑁𝑑 PROPN cana-3678 86 4 βˆ’ βˆ’ NOUN cana-3678 86 5 πœŒπ‘‘ πœŒπ‘‘ ADV cana-3678 86 6 is be AUX cana-3678 86 7 the the DET cana-3678 86 8 compensated compensated ADJ cana-3678 86 9 poisson poisson NOUN cana-3678 86 10 process process NOUN cana-3678 86 11 where where SCONJ cana-3678 86 12 𝑁𝑑 𝑁𝑑 PROPN cana-3678 86 13 is be AUX cana-3678 86 14 a a DET cana-3678 86 15 poisson poisson NOUN cana-3678 86 16 process process NOUN cana-3678 86 17 with with ADP cana-3678 86 18 deterministic deterministic ADJ cana-3678 86 19 intensity intensity NOUN cana-3678 86 20 𝜌 𝜌 ADP cana-3678 86 21 , , PUNCT cana-3678 86 22 πœ‚π‘‘ πœ‚π‘‘ ADP cana-3678 86 23 and and CCONJ cana-3678 86 24 πœπ‘‘ πœπ‘‘ PROPN cana-3678 86 25 are be AUX cana-3678 86 26 adapted adapt VERB cana-3678 86 27 process process NOUN cana-3678 86 28 to to ADP cana-3678 86 29 a a DET cana-3678 86 30 filtration filtration NOUN cana-3678 86 31 generated generate VERB cana-3678 86 32 by by ADP cana-3678 86 33 the the DET cana-3678 86 34 brownian brownian PROPN cana-3678 86 35 motion motion NOUN cana-3678 86 36 , , PUNCT cana-3678 86 37 πœ†(𝑑 πœ†(𝑑 PROPN cana-3678 86 38 , , PUNCT cana-3678 86 39 𝑆𝑑 𝑆𝑑 PROPN cana-3678 86 40 ) ) PUNCT cana-3678 86 41 is be AUX cana-3678 86 42 price price NOUN cana-3678 86 43 impact impact NOUN cana-3678 86 44 function function NOUN cana-3678 86 45 of of ADP cana-3678 86 46 the the DET cana-3678 86 47 trader trader NOUN cana-3678 86 48 ( ( PUNCT cana-3678 86 49 non non ADJ cana-3678 86 50 - - ADJ cana-3678 86 51 negative negative ADJ cana-3678 86 52 ) ) PUNCT cana-3678 86 53 and and CCONJ cana-3678 86 54 πœƒπ‘‘ πœƒπ‘‘ ADV cana-3678 86 55 is be VERB cana-3678 86 56 the the DET cana-3678 86 57 number number NOUN cana-3678 86 58 of of ADP cana-3678 86 59 shares share NOUN cana-3678 86 60 . . PUNCT cana-3678 87 1 theorem theorem VERB cana-3678 87 2 : : PUNCT cana-3678 87 3 the the DET cana-3678 87 4 nonlinear nonlinear ADJ cana-3678 87 5 partial partial ADJ cana-3678 87 6 differential differential NOUN cana-3678 87 7 equation equation NOUN cana-3678 87 8 of of ADP cana-3678 87 9 black black ADJ cana-3678 87 10 - - PUNCT cana-3678 87 11 scholes schole NOUN cana-3678 87 12 with with ADP cana-3678 87 13 transaction transaction NOUN cana-3678 87 14 costs cost NOUN cana-3678 87 15 in in ADP cana-3678 87 16 illiquid illiquid ADJ cana-3678 87 17 market market NOUN cana-3678 87 18 with with ADP cana-3678 87 19 jumps jump NOUN cana-3678 87 20 for for ADP cana-3678 87 21 the the DET cana-3678 87 22 european european ADJ cana-3678 87 23 call call NOUN cana-3678 87 24 option option NOUN cana-3678 87 25 price price NOUN cana-3678 87 26 𝐢(𝑑 𝐢(𝑑 NOUN cana-3678 87 27 , , PUNCT cana-3678 87 28 𝑆𝑑 𝑆𝑑 PROPN cana-3678 87 29 ) ) PUNCT cana-3678 87 30 at at ADP cana-3678 87 31 time time NOUN cana-3678 87 32 𝑑 𝑑 PROPN cana-3678 87 33 ∈ ∈ PROPN cana-3678 88 1 [ [ X cana-3678 88 2 0 0 NUM cana-3678 88 3 , , PUNCT cana-3678 88 4 𝑇 𝑇 PROPN cana-3678 88 5 ] ] PUNCT cana-3678 88 6 and and CCONJ cana-3678 88 7 stock stock NOUN cana-3678 88 8 value value NOUN cana-3678 88 9 𝑆𝑑 𝑆𝑑 PROPN cana-3678 88 10 satisfies satisfy VERB cana-3678 88 11 the the DET cana-3678 88 12 equation equation NOUN cana-3678 88 13 ( ( PUNCT cana-3678 88 14 3 3 NUM cana-3678 88 15 ) ) PUNCT cana-3678 88 16 and and CCONJ cana-3678 88 17 ( ( PUNCT cana-3678 88 18 4 4 X cana-3678 88 19 ) ) PUNCT cana-3678 88 20 is be AUX cana-3678 88 21 given give VERB cana-3678 88 22 by by ADP cana-3678 88 23 communications communication NOUN cana-3678 88 24 on on ADP cana-3678 88 25 applied apply VERB cana-3678 88 26 nonlinear nonlinear ADJ cana-3678 88 27 analysis analysis NOUN cana-3678 88 28 issn issn NOUN cana-3678 88 29 : : PUNCT cana-3678 88 30 1074 1074 NUM cana-3678 88 31 - - PUNCT cana-3678 88 32 133x 133x NUM cana-3678 88 33 vol vol NOUN cana-3678 88 34 32 32 NUM cana-3678 88 35 no no NOUN cana-3678 88 36 . . PUNCT cana-3678 89 1 8s 8s PROPN cana-3678 89 2 ( ( PUNCT cana-3678 89 3 2025 2025 NUM cana-3678 89 4 ) ) PUNCT cana-3678 89 5 323 323 NUM cana-3678 89 6 https://internationalpubls.com https://internationalpubls.com X cana-3678 89 7 π‘Ÿ(𝑑 π‘Ÿ(𝑑 NOUN cana-3678 89 8 , , PUNCT cana-3678 89 9 𝑆𝑑)𝑉𝑑 𝑆𝑑)𝑉𝑑 CCONJ cana-3678 90 1 + + CCONJ cana-3678 90 2 πœƒπ‘‘π‘†π‘‘[πœ‡(𝑑 πœƒπ‘‘π‘†π‘‘[πœ‡(𝑑 ADJ cana-3678 90 3 , , PUNCT cana-3678 90 4 𝑆𝑑 𝑆𝑑 PROPN cana-3678 90 5 ) ) PUNCT cana-3678 90 6 βˆ’ βˆ’ NOUN cana-3678 90 7 π‘Ÿ(𝑑 π‘Ÿ(𝑑 NOUN cana-3678 90 8 , , PUNCT cana-3678 90 9 𝑆𝑑 𝑆𝑑 PROPN cana-3678 90 10 ) ) PUNCT cana-3678 91 1 + + CCONJ cana-3678 91 2 πœ†(𝑑 πœ†(𝑑 PROPN cana-3678 91 3 , , PUNCT cana-3678 91 4 𝑆𝑑)πœ‚π‘‘ 𝑆𝑑)πœ‚π‘‘ PROPN cana-3678 91 5 + + X cana-3678 91 6 π‘˜(𝑑 π‘˜(𝑑 PROPN cana-3678 91 7 , , PUNCT cana-3678 91 8 𝑆𝑑)πœ‚π‘‘ 𝑆𝑑)πœ‚π‘‘ NOUN cana-3678 91 9 ] ] X cana-3678 91 10 = = SYM cana-3678 91 11 πœ•π‘‘πΆ(𝑑 πœ•π‘‘πΆ(𝑑 NOUN cana-3678 91 12 , , PUNCT cana-3678 91 13 𝑆𝑑 𝑆𝑑 PROPN cana-3678 91 14 ) ) PUNCT cana-3678 91 15 + + CCONJ cana-3678 91 16 ( ( PUNCT cana-3678 91 17 πœ‡(𝑑 πœ‡(𝑑 NOUN cana-3678 91 18 , , PUNCT cana-3678 91 19 𝑆𝑑 𝑆𝑑 PROPN cana-3678 91 20 ) ) PUNCT cana-3678 91 21 + + CCONJ cana-3678 92 1 πœ†(𝑑 πœ†(𝑑 PROPN cana-3678 92 2 , , PUNCT cana-3678 92 3 𝑆𝑑)πœ‚π‘‘ 𝑆𝑑)πœ‚π‘‘ PROPN cana-3678 92 4 + + X cana-3678 92 5 π‘˜(𝑑 π‘˜(𝑑 PROPN cana-3678 92 6 , , PUNCT cana-3678 92 7 𝑆𝑑)πœ‚π‘‘ 𝑆𝑑)πœ‚π‘‘ PROPN cana-3678 92 8 βˆ’ βˆ’ PROPN cana-3678 92 9 𝜌[π‘ŽπœŽ(𝑑 𝜌[π‘ŽπœŽ(𝑑 PROPN cana-3678 92 10 , , PUNCT cana-3678 92 11 𝑆𝑑 𝑆𝑑 PROPN cana-3678 92 12 ) ) PUNCT cana-3678 92 13 + + CCONJ cana-3678 92 14 π‘πœ†(𝑑 π‘πœ†(𝑑 NOUN cana-3678 92 15 , , PUNCT cana-3678 92 16 𝑆𝑑)πœπ‘‘ 𝑆𝑑)πœπ‘‘ NOUN cana-3678 92 17 + + CCONJ cana-3678 92 18 π‘π‘˜(𝑑 π‘π‘˜(𝑑 NOUN cana-3678 92 19 , , PUNCT cana-3678 92 20 𝑆𝑑)πœπ‘‘])π‘†π‘‘πœ•π‘ πΆ(𝑑 𝑆𝑑)πœπ‘‘])π‘†π‘‘πœ•π‘ πΆ(𝑑 PROPN cana-3678 92 21 , , PUNCT cana-3678 92 22 𝑆𝑑 𝑆𝑑 PROPN cana-3678 92 23 ) ) PUNCT cana-3678 92 24 + + CCONJ cana-3678 92 25 1 1 NUM cana-3678 92 26 2 2 NUM cana-3678 92 27 ( ( PUNCT cana-3678 92 28 𝜎(𝑑 𝜎(𝑑 NUM cana-3678 92 29 , , PUNCT cana-3678 92 30 𝑆𝑑 𝑆𝑑 PROPN cana-3678 92 31 ) ) PUNCT cana-3678 92 32 + + NOUN cana-3678 92 33 πœ†(𝑑 πœ†(𝑑 PROPN cana-3678 92 34 , , PUNCT cana-3678 92 35 𝑆𝑑)πœπ‘‘ 𝑆𝑑)πœπ‘‘ NOUN cana-3678 92 36 + + CCONJ cana-3678 92 37 π‘˜(𝑑 π‘˜(𝑑 PROPN cana-3678 92 38 , , PUNCT cana-3678 92 39 𝑆𝑑)πœπ‘‘)2𝑆𝑑 𝑆𝑑)πœπ‘‘)2𝑆𝑑 PROPN cana-3678 92 40 2πœ•π‘ π‘  2πœ•π‘ π‘  NOUN cana-3678 92 41 2 2 NUM cana-3678 92 42 𝐢(𝑑 𝐢(𝑑 NOUN cana-3678 92 43 , , PUNCT cana-3678 92 44 𝑆𝑑 𝑆𝑑 PROPN cana-3678 92 45 ) ) PUNCT cana-3678 92 46 + + CCONJ cana-3678 92 47 𝜌 𝜌 X cana-3678 92 48 ( ( PUNCT cana-3678 92 49 𝐢(𝑑 𝐢(𝑑 X cana-3678 92 50 , , PUNCT cana-3678 92 51 𝑆𝑑 𝑆𝑑 PROPN cana-3678 92 52 βˆ’(1 βˆ’(1 NOUN cana-3678 92 53 + + CCONJ cana-3678 92 54 π‘ŽπœŽ(𝑑 π‘ŽπœŽ(𝑑 NUM cana-3678 92 55 , , PUNCT cana-3678 92 56 𝑆𝑑 𝑆𝑑 PROPN cana-3678 92 57 ) ) PUNCT cana-3678 92 58 + + CCONJ cana-3678 92 59 π‘πœ†(𝑑 π‘πœ†(𝑑 NOUN cana-3678 92 60 , , PUNCT cana-3678 92 61 𝑆𝑑)πœπ‘‘ 𝑆𝑑)πœπ‘‘ NOUN cana-3678 92 62 + + CCONJ cana-3678 92 63 π‘π‘˜(𝑑 π‘π‘˜(𝑑 NOUN cana-3678 92 64 , , PUNCT cana-3678 92 65 𝑆𝑑)πœπ‘‘ 𝑆𝑑)πœπ‘‘ NOUN cana-3678 92 66 ) ) PUNCT cana-3678 92 67 ) ) PUNCT cana-3678 92 68 βˆ’ βˆ’ PROPN cana-3678 93 1 𝐢(𝑑 𝐢(𝑑 NOUN cana-3678 93 2 , , PUNCT cana-3678 93 3 𝑆𝑑 𝑆𝑑 PROPN cana-3678 93 4 βˆ’ βˆ’ NOUN cana-3678 93 5 ) ) PUNCT cana-3678 93 6 ) ) PUNCT cana-3678 93 7 ( ( PUNCT cana-3678 93 8 5 5 X cana-3678 93 9 ) ) PUNCT cana-3678 93 10 with with ADP cana-3678 93 11 the the DET cana-3678 93 12 terminal terminal ADJ cana-3678 93 13 condition condition NOUN cana-3678 93 14 𝐢(𝑇,𝑆𝑇 𝐢(𝑇,𝑆𝑇 NOUN cana-3678 93 15 ) ) PUNCT cana-3678 93 16 = = SYM cana-3678 93 17 β„Ž(𝑆𝑇 β„Ž(𝑆𝑇 PROPN cana-3678 93 18 ) ) PUNCT cana-3678 93 19 . . PUNCT cana-3678 94 1 in in ADP cana-3678 94 2 the the DET cana-3678 94 3 above above ADJ cana-3678 94 4 equation equation NOUN cana-3678 94 5 put put VERB cana-3678 94 6 a a DET cana-3678 94 7 = = NOUN cana-3678 94 8 b=0 b=0 PROPN cana-3678 94 9 , , PUNCT cana-3678 94 10 i.e. i.e. X cana-3678 94 11 jump jump NOUN cana-3678 94 12 is be AUX cana-3678 94 13 cancelled cancel VERB cana-3678 94 14 . . PUNCT cana-3678 95 1 we we PRON cana-3678 95 2 get get VERB cana-3678 95 3 nonlinear nonlinear ADJ cana-3678 95 4 transaction transaction NOUN cana-3678 95 5 cost cost NOUN cana-3678 95 6 model model NOUN cana-3678 95 7 ( ( PUNCT cana-3678 95 8 partial partial ADJ cana-3678 95 9 differential differential NOUN cana-3678 95 10 equation equation NOUN cana-3678 95 11 ) ) PUNCT cana-3678 95 12 in in ADP cana-3678 95 13 illiquid illiquid ADJ cana-3678 95 14 market market NOUN cana-3678 95 15 mentioned mention VERB cana-3678 95 16 below below ADV cana-3678 95 17 . . PUNCT cana-3678 96 1 βˆ‚πΆ βˆ‚πΆ ADP cana-3678 96 2 βˆ‚π‘‘ βˆ‚π‘‘ PROPN cana-3678 97 1 + + PROPN cana-3678 97 2 Οƒ Οƒ PROPN cana-3678 97 3 2𝑆2 2𝑆2 NUM cana-3678 97 4 2[1βˆ’Ξ»(𝑑,𝑆𝑑 2[1βˆ’Ξ»(𝑑,𝑆𝑑 NUM cana-3678 97 5 ) ) PUNCT cana-3678 98 1 + + NOUN cana-3678 98 2 π‘˜(𝑑,𝑆𝑑 π‘˜(𝑑,𝑆𝑑 PROPN cana-3678 98 3 ) ) PUNCT cana-3678 99 1 𝑆 𝑆 PROPN cana-3678 99 2 βˆ‚2𝐢 βˆ‚2𝐢 NOUN cana-3678 99 3 βˆ‚π‘†2 βˆ‚π‘†2 ADJ cana-3678 99 4 ] ] SYM cana-3678 99 5 2 2 NUM cana-3678 99 6 βˆ‚2𝐢 βˆ‚2𝐢 NOUN cana-3678 99 7 βˆ‚π‘†2 βˆ‚π‘†2 ADJ cana-3678 99 8 + + NOUN cana-3678 99 9 π‘Ÿπ‘† π‘Ÿπ‘† NOUN cana-3678 99 10 βˆ‚πΆ βˆ‚πΆ ADP cana-3678 99 11 βˆ‚π‘† βˆ‚π‘† PROPN cana-3678 99 12 βˆ’ βˆ’ PROPN cana-3678 99 13 π‘ŸπΆ π‘ŸπΆ PROPN cana-3678 99 14 = = SYM cana-3678 99 15 0 0 NUM cana-3678 100 1 ( ( PUNCT cana-3678 100 2 6 6 NUM cana-3678 100 3 ) ) PUNCT cana-3678 100 4 with with ADP cana-3678 100 5 the the DET cana-3678 100 6 terminal terminal ADJ cana-3678 100 7 and and CCONJ cana-3678 100 8 boundary boundary ADJ cana-3678 100 9 conditions condition NOUN cana-3678 100 10 for for ADP cana-3678 100 11 european european ADJ cana-3678 100 12 call call NOUN cana-3678 100 13 options option NOUN cana-3678 100 14 𝐢(𝑇 𝐢(𝑇 PROPN cana-3678 100 15 , , PUNCT cana-3678 100 16 𝑆(𝑇 𝑆(𝑇 PROPN cana-3678 100 17 ) ) PUNCT cana-3678 100 18 ) ) PUNCT cana-3678 101 1 = = PUNCT cana-3678 101 2 π‘šπ‘Žπ‘₯(𝑆(𝑑 π‘šπ‘Žπ‘₯(𝑆(𝑑 ADJ cana-3678 101 3 ) ) PUNCT cana-3678 101 4 βˆ’ βˆ’ PROPN cana-3678 101 5 𝐾 𝐾 PROPN cana-3678 101 6 , , PUNCT cana-3678 101 7 0 0 NUM cana-3678 101 8 ) ) PUNCT cana-3678 101 9 𝐢(𝑑 𝐢(𝑑 NUM cana-3678 101 10 , , PUNCT cana-3678 101 11 𝐿 𝐿 PROPN cana-3678 101 12 ) ) PUNCT cana-3678 101 13 = = SYM cana-3678 101 14 𝐿 𝐿 PROPN cana-3678 101 15 βˆ’ βˆ’ PROPN cana-3678 101 16 πΎπ‘’βˆ’π‘Ÿ(π‘‡βˆ’π‘‘ πΎπ‘’βˆ’π‘Ÿ(π‘‡βˆ’π‘‘ NOUN cana-3678 101 17 ) ) PUNCT cana-3678 101 18 , , PUNCT cana-3678 101 19 ( ( PUNCT cana-3678 101 20 βˆ€πΏ βˆ€πΏ PROPN cana-3678 101 21 > > X cana-3678 101 22 𝑆(𝑇 𝑆(𝑇 PROPN cana-3678 101 23 ) ) PUNCT cana-3678 101 24 ) ) PUNCT cana-3678 102 1 𝐢(𝑑 𝐢(𝑑 ADP cana-3678 102 2 , , PUNCT cana-3678 102 3 0 0 NUM cana-3678 102 4 ) ) PUNCT cana-3678 102 5 = = SYM cana-3678 102 6 0 0 PUNCT cana-3678 103 1 the the DET cana-3678 103 2 objective objective NOUN cana-3678 103 3 of of ADP cana-3678 103 4 the the DET cana-3678 103 5 paper paper NOUN cana-3678 103 6 is be AUX cana-3678 103 7 to to PART cana-3678 103 8 solve solve VERB cana-3678 103 9 the the DET cana-3678 103 10 above above ADJ cana-3678 103 11 nonlinear nonlinear ADJ cana-3678 103 12 partial partial ADJ cana-3678 103 13 differential differential NOUN cana-3678 103 14 equation equation NOUN cana-3678 103 15 using use VERB cana-3678 103 16 soft soft ADJ cana-3678 103 17 computing computing NOUN cana-3678 103 18 technique technique NOUN cana-3678 103 19 like like ADP cana-3678 103 20 deep deep ADJ cana-3678 103 21 learning learning NOUN cana-3678 103 22 based base VERB cana-3678 103 23 fully fully ADV cana-3678 103 24 connected connect VERB cana-3678 103 25 neural neural ADJ cana-3678 103 26 network network NOUN cana-3678 103 27 ( ( PUNCT cana-3678 103 28 fcnn fcnn PROPN cana-3678 103 29 ) ) PUNCT cana-3678 103 30 with with ADP cana-3678 103 31 good good ADJ cana-3678 103 32 accuracy accuracy NOUN cana-3678 103 33 . . PUNCT cana-3678 104 1 3 3 X cana-3678 104 2 . . X cana-3678 104 3 methods method NOUN cana-3678 104 4 to to PART cana-3678 104 5 find find VERB cana-3678 104 6 the the DET cana-3678 104 7 solution solution NOUN cana-3678 104 8 of of ADP cana-3678 104 9 the the DET cana-3678 104 10 above above ADJ cana-3678 104 11 nonlinear nonlinear PROPN cana-3678 104 12 model model NOUN cana-3678 104 13 , , PUNCT cana-3678 104 14 the the DET cana-3678 104 15 procedure procedure NOUN cana-3678 104 16 is be AUX cana-3678 104 17 divided divide VERB cana-3678 104 18 in in ADP cana-3678 104 19 two two NUM cana-3678 104 20 parts part NOUN cana-3678 104 21 . . PUNCT cana-3678 105 1 ( ( PUNCT cana-3678 105 2 1 1 X cana-3678 105 3 ) ) PUNCT cana-3678 105 4 convert convert VERB cana-3678 105 5 the the DET cana-3678 105 6 nonlinear nonlinear ADJ cana-3678 105 7 partial partial ADJ cana-3678 105 8 differential differential NOUN cana-3678 105 9 equation equation NOUN cana-3678 105 10 of of ADP cana-3678 105 11 black black ADJ cana-3678 105 12 - - PUNCT cana-3678 105 13 scholes schole NOUN cana-3678 105 14 with with ADP cana-3678 105 15 transaction transaction NOUN cana-3678 105 16 costs cost NOUN cana-3678 105 17 in in ADP cana-3678 105 18 illiquid illiquid ADJ cana-3678 105 19 market market NOUN cana-3678 105 20 into into ADP cana-3678 105 21 nonlinear nonlinear ADJ cana-3678 105 22 ordinary ordinary ADJ cana-3678 105 23 differential differential ADJ cana-3678 105 24 equation equation NOUN cana-3678 105 25 : : PUNCT cana-3678 105 26 first first ADV cana-3678 105 27 the the DET cana-3678 105 28 nonlinear nonlinear ADJ cana-3678 105 29 partial partial ADJ cana-3678 105 30 differential differential NOUN cana-3678 105 31 equation equation NOUN cana-3678 105 32 is be AUX cana-3678 105 33 converted convert VERB cana-3678 105 34 into into ADP cana-3678 105 35 nonlinear nonlinear ADJ cana-3678 105 36 ordinary ordinary ADJ cana-3678 105 37 differential differential ADJ cana-3678 105 38 equation equation NOUN cana-3678 105 39 with with ADP cana-3678 105 40 semi semi ADJ cana-3678 105 41 discretization discretization NOUN cana-3678 105 42 finite finite ADJ cana-3678 105 43 difference difference NOUN cana-3678 105 44 technique technique NOUN cana-3678 105 45 ( ( PUNCT cana-3678 105 46 [ [ X cana-3678 105 47 25 25 NUM cana-3678 105 48 ] ] PUNCT cana-3678 105 49 ) ) PUNCT cana-3678 105 50 . . PUNCT cana-3678 106 1 this this DET cana-3678 106 2 method method NOUN cana-3678 106 3 is be AUX cana-3678 106 4 also also ADV cana-3678 106 5 known know VERB cana-3678 106 6 as as ADP cana-3678 106 7 the the DET cana-3678 106 8 method method NOUN cana-3678 106 9 of of ADP cana-3678 106 10 lines line NOUN cana-3678 106 11 . . PUNCT cana-3678 107 1 discretize discretize NOUN cana-3678 107 2 s s VERB cana-3678 107 3 in in ADP cana-3678 107 4 the the DET cana-3678 107 5 interval interval NOUN cana-3678 107 6 [ [ X cana-3678 107 7 0 0 NUM cana-3678 107 8 , , PUNCT cana-3678 107 9 π‘†π‘šπ‘Žπ‘₯ π‘†π‘šπ‘Žπ‘₯ PROPN cana-3678 107 10 ] ] PUNCT cana-3678 107 11 into into ADP cana-3678 107 12 n n CCONJ cana-3678 107 13 equal equal ADJ cana-3678 107 14 parts part NOUN cana-3678 107 15 with with ADP cana-3678 107 16 grid grid NOUN cana-3678 107 17 size size NOUN cana-3678 107 18 βˆ†π‘† βˆ†π‘† PROPN cana-3678 107 19 = = SYM cana-3678 107 20 π‘†π‘šπ‘Žπ‘₯ π‘†π‘šπ‘Žπ‘₯ PROPN cana-3678 107 21 𝑁 𝑁 PROPN cana-3678 107 22 . . PUNCT cana-3678 108 1 first first PROPN cana-3678 108 2 spatial spatial ADJ cana-3678 108 3 derivative derivative ADJ cana-3678 108 4 and and CCONJ cana-3678 108 5 second second ADJ cana-3678 108 6 spatial spatial ADJ cana-3678 108 7 derivative derivative NOUN cana-3678 108 8 in in ADP cana-3678 108 9 equation equation NOUN cana-3678 108 10 ( ( PUNCT cana-3678 108 11 6 6 NUM cana-3678 108 12 ) ) PUNCT cana-3678 108 13 are be AUX cana-3678 108 14 approximated approximate VERB cana-3678 108 15 by by ADP cana-3678 108 16 central central ADJ cana-3678 108 17 finite finite ADJ cana-3678 108 18 differences difference NOUN cana-3678 108 19 with with ADP cana-3678 108 20 second second ADJ cana-3678 108 21 order order NOUN cana-3678 108 22 . . PUNCT cana-3678 109 1 let let VERB cana-3678 109 2 𝐢𝑖(𝑑 𝐢𝑖(𝑑 NUM cana-3678 109 3 , , PUNCT cana-3678 109 4 𝑆𝑖 𝑆𝑖 PROPN cana-3678 109 5 ) ) PUNCT cana-3678 109 6 be be VERB cana-3678 109 7 the the DET cana-3678 109 8 approximation approximation NOUN cana-3678 109 9 of of ADP cana-3678 109 10 option option NOUN cana-3678 109 11 value value NOUN cana-3678 109 12 . . PUNCT cana-3678 110 1 also also ADV cana-3678 110 2 take take VERB cana-3678 110 3 πœ†π‘–(𝑑 πœ†π‘–(𝑑 NOUN cana-3678 110 4 , , PUNCT cana-3678 110 5 𝑆(𝑑 𝑆(𝑑 NOUN cana-3678 110 6 ) ) PUNCT cana-3678 110 7 ) ) PUNCT cana-3678 111 1 = = SYM cana-3678 111 2 πœ— πœ— X cana-3678 111 3 the the DET cana-3678 111 4 liquidity liquidity NOUN cana-3678 111 5 parameter parameter NOUN cana-3678 111 6 and and CCONJ cana-3678 111 7 𝐾𝑖(𝑑 𝐾𝑖(𝑑 NUM cana-3678 111 8 , , PUNCT cana-3678 111 9 𝑆(𝑑 𝑆(𝑑 NUM cana-3678 111 10 ) ) PUNCT cana-3678 111 11 ) ) PUNCT cana-3678 112 1 = = SYM cana-3678 112 2 𝑆𝑖 𝑆𝑖 PROPN cana-3678 112 3 π‘ž π‘ž X cana-3678 112 4 2π‘’π‘Ÿ(π‘‡βˆ’π‘‘ 2π‘’π‘Ÿ(π‘‡βˆ’π‘‘ NUM cana-3678 112 5 ) ) PUNCT cana-3678 112 6 2 2 NUM cana-3678 112 7 is be AUX cana-3678 112 8 the the DET cana-3678 112 9 transaction transaction NOUN cana-3678 112 10 costs cost NOUN cana-3678 112 11 where where SCONJ cana-3678 112 12 q q NOUN cana-3678 112 13 is be AUX cana-3678 112 14 the the DET cana-3678 112 15 proportional proportional ADJ cana-3678 112 16 transaction transaction NOUN cana-3678 112 17 cost cost NOUN cana-3678 112 18 ( ( PUNCT cana-3678 112 19 [ [ X cana-3678 112 20 26 26 NUM cana-3678 112 21 ] ] PUNCT cana-3678 112 22 ) ) PUNCT cana-3678 112 23 . . PUNCT cana-3678 113 1 𝑑𝐢𝑖 𝑑𝐢𝑖 NOUN cana-3678 113 2 𝑑𝑑 𝑑𝑑 ADP cana-3678 113 3 + + NUM cana-3678 113 4 𝜎2𝑆𝑖 𝜎2𝑆𝑖 PROPN cana-3678 113 5 2 2 NUM cana-3678 113 6 2[1βˆ’{πœ†(𝑑,𝑆𝑑)+π‘˜(𝑑,𝑆𝑑)}𝑆𝑖 2[1βˆ’{πœ†(𝑑,𝑆𝑑)+π‘˜(𝑑,𝑆𝑑)}𝑆𝑖 NUM cana-3678 113 7 } } PUNCT cana-3678 113 8 ( ( PUNCT cana-3678 113 9 𝐢𝑖+1 𝐢𝑖+1 X cana-3678 113 10 βˆ’2 βˆ’2 NOUN cana-3678 113 11 𝐢𝑖 𝐢𝑖 PROPN cana-3678 113 12 + + CCONJ cana-3678 113 13 πΆπ‘–βˆ’1 πΆπ‘–βˆ’1 NOUN cana-3678 113 14 ( ( PUNCT cana-3678 113 15 βˆ†π‘†)2 βˆ†π‘†)2 PROPN cana-3678 113 16 ) ) PUNCT cana-3678 113 17 ] ] PUNCT cana-3678 113 18 2 2 NUM cana-3678 113 19 ( ( PUNCT cana-3678 113 20 𝐢𝑖+1 𝐢𝑖+1 X cana-3678 113 21 βˆ’2 βˆ’2 NOUN cana-3678 113 22 𝐢𝑖 𝐢𝑖 PROPN cana-3678 114 1 + + CCONJ cana-3678 114 2 πΆπ‘–βˆ’1 πΆπ‘–βˆ’1 NOUN cana-3678 114 3 ( ( PUNCT cana-3678 114 4 βˆ†π‘†)2 βˆ†π‘†)2 PROPN cana-3678 114 5 ) ) PUNCT cana-3678 115 1 + + CCONJ cana-3678 115 2 π‘Ÿπ‘†π‘– π‘Ÿπ‘†π‘– PRON cana-3678 115 3 ( ( PUNCT cana-3678 115 4 c𝑖+1βˆ’ c𝑖+1βˆ’ NOUN cana-3678 115 5 𝐢𝑖 𝐢𝑖 ADP cana-3678 115 6 βˆ’1 βˆ’1 NOUN cana-3678 115 7 2βˆ†π‘† 2βˆ†π‘† NUM cana-3678 115 8 ) ) PUNCT cana-3678 115 9 βˆ’ βˆ’ PROPN cana-3678 115 10 π‘ŸπΆπ‘– π‘ŸπΆπ‘– NUM cana-3678 115 11 = = SYM cana-3678 115 12 0 0 NUM cana-3678 115 13 ( ( PUNCT cana-3678 115 14 7 7 NUM cana-3678 115 15 ) ) PUNCT cana-3678 115 16 with with ADP cana-3678 115 17 the the DET cana-3678 115 18 terminal terminal ADJ cana-3678 115 19 and and CCONJ cana-3678 115 20 boundary boundary ADJ cana-3678 115 21 conditions condition NOUN cana-3678 115 22 for for ADP cana-3678 115 23 the the DET cana-3678 115 24 european european ADJ cana-3678 115 25 call call NOUN cana-3678 115 26 option option NOUN cana-3678 115 27 given give VERB cana-3678 115 28 as as ADP cana-3678 115 29 𝐢(𝑇 𝐢(𝑇 NUM cana-3678 115 30 , , PUNCT cana-3678 115 31 𝑆(𝑇 𝑆(𝑇 PROPN cana-3678 115 32 ) ) PUNCT cana-3678 115 33 ) ) PUNCT cana-3678 115 34 = = SYM cana-3678 115 35 π‘šπ‘Žπ‘₯(𝑆𝑖(𝑑 π‘šπ‘Žπ‘₯(𝑆𝑖(𝑑 X cana-3678 115 36 ) ) PUNCT cana-3678 115 37 βˆ’ βˆ’ PROPN cana-3678 115 38 𝐾 𝐾 PROPN cana-3678 115 39 , , PUNCT cana-3678 115 40 0 0 NUM cana-3678 115 41 ) ) PUNCT cana-3678 115 42 𝐢(𝑑 𝐢(𝑑 NUM cana-3678 115 43 , , PUNCT cana-3678 115 44 𝐿 𝐿 PROPN cana-3678 115 45 ) ) PUNCT cana-3678 115 46 = = SYM cana-3678 115 47 π‘†π‘šπ‘Žπ‘₯ π‘†π‘šπ‘Žπ‘₯ PROPN cana-3678 115 48 βˆ’ βˆ’ PROPN cana-3678 115 49 πΎπ‘’βˆ’π‘Ÿ(π‘‡βˆ’π‘‘ πΎπ‘’βˆ’π‘Ÿ(π‘‡βˆ’π‘‘ NOUN cana-3678 115 50 ) ) PUNCT cana-3678 115 51 , , PUNCT cana-3678 115 52 ( ( PUNCT cana-3678 115 53 βˆ€πΏ βˆ€πΏ PROPN cana-3678 115 54 > > X cana-3678 115 55 𝑆(𝑇 𝑆(𝑇 PROPN cana-3678 115 56 ) ) PUNCT cana-3678 115 57 ) ) PUNCT cana-3678 116 1 ( ( PUNCT cana-3678 116 2 8) 8) NUM cana-3678 116 3 communications communication NOUN cana-3678 116 4 on on ADP cana-3678 116 5 applied apply VERB cana-3678 116 6 nonlinear nonlinear ADJ cana-3678 116 7 analysis analysis NOUN cana-3678 116 8 issn issn NOUN cana-3678 116 9 : : PUNCT cana-3678 116 10 1074 1074 NUM cana-3678 116 11 - - PUNCT cana-3678 116 12 133x 133x NUM cana-3678 116 13 vol vol NOUN cana-3678 116 14 32 32 NUM cana-3678 116 15 no no NOUN cana-3678 116 16 . . PUNCT cana-3678 117 1 8s 8s PROPN cana-3678 117 2 ( ( PUNCT cana-3678 117 3 2025 2025 NUM cana-3678 117 4 ) ) PUNCT cana-3678 117 5 324 324 NUM cana-3678 117 6 https://internationalpubls.com https://internationalpubls.com X cana-3678 117 7 𝐢(𝑑 𝐢(𝑑 X cana-3678 117 8 , , PUNCT cana-3678 117 9 0 0 NUM cana-3678 117 10 ) ) PUNCT cana-3678 117 11 = = SYM cana-3678 117 12 0 0 PUNCT cana-3678 118 1 ( ( PUNCT cana-3678 118 2 2 2 NUM cana-3678 118 3 ) ) PUNCT cana-3678 118 4 converted convert VERB cana-3678 118 5 nonlinear nonlinear ADJ cana-3678 118 6 ordinary ordinary ADJ cana-3678 118 7 differential differential ADJ cana-3678 118 8 equation equation NOUN cana-3678 118 9 is be AUX cana-3678 118 10 solved solve VERB cana-3678 118 11 using use VERB cana-3678 118 12 the the DET cana-3678 118 13 deep deep ADJ cana-3678 118 14 learning learning NOUN cana-3678 118 15 - - PUNCT cana-3678 118 16 based base VERB cana-3678 118 17 algorithm algorithm NOUN cana-3678 118 18 of of ADP cana-3678 118 19 fully fully ADV cana-3678 118 20 connected connected ADJ cana-3678 118 21 neural neural ADJ cana-3678 118 22 network network NOUN cana-3678 118 23 ( ( PUNCT cana-3678 118 24 fcnn fcnn ADJ cana-3678 118 25 ): ): PUNCT cana-3678 118 26 equation equation NOUN cana-3678 118 27 ( ( PUNCT cana-3678 118 28 7 7 NUM cana-3678 118 29 ) ) PUNCT cana-3678 118 30 with with ADP cana-3678 118 31 given give VERB cana-3678 118 32 conditions condition NOUN cana-3678 118 33 in in ADP cana-3678 118 34 equation equation NOUN cana-3678 118 35 ( ( PUNCT cana-3678 118 36 8) 8) NUM cana-3678 118 37 is be AUX cana-3678 118 38 now now ADV cana-3678 118 39 solved solve VERB cana-3678 118 40 using use VERB cana-3678 118 41 fcnn fcnn NOUN cana-3678 118 42 with with ADP cana-3678 118 43 deep deep ADJ cana-3678 118 44 learning learning NOUN cana-3678 118 45 . . PUNCT cana-3678 119 1 fcnn fcnn NOUN cana-3678 119 2 refers refer VERB cana-3678 119 3 to to ADP cana-3678 119 4 fully fully ADV cana-3678 119 5 connected connect VERB cana-3678 119 6 neural neural ADJ cana-3678 119 7 network network NOUN cana-3678 119 8 ( ( PUNCT cana-3678 119 9 fcnn fcnn PROPN cana-3678 119 10 ) ) PUNCT cana-3678 119 11 , , PUNCT cana-3678 119 12 a a DET cana-3678 119 13 specific specific ADJ cana-3678 119 14 architecture architecture NOUN cana-3678 119 15 within within ADP cana-3678 119 16 deep deep ADJ cana-3678 119 17 learning learning NOUN cana-3678 119 18 . . PUNCT cana-3678 120 1 it it PRON cana-3678 120 2 is be AUX cana-3678 120 3 among among ADP cana-3678 120 4 the the DET cana-3678 120 5 easiest easy ADJ cana-3678 120 6 and and CCONJ cana-3678 120 7 most most ADV cana-3678 120 8 frequently frequently ADV cana-3678 120 9 utilized utilize VERB cana-3678 120 10 forms form NOUN cana-3678 120 11 of of ADP cana-3678 120 12 neural neural ADJ cana-3678 120 13 networks network NOUN cana-3678 120 14 , , PUNCT cana-3678 120 15 usually usually ADV cana-3678 120 16 used use VERB cana-3678 120 17 for for ADP cana-3678 120 18 purposes purpose NOUN cana-3678 120 19 such such ADJ cana-3678 120 20 as as ADP cana-3678 120 21 regression regression NOUN cana-3678 120 22 , , PUNCT cana-3678 120 23 class class NOUN cana-3678 120 24 ification ification NOUN cana-3678 120 25 , , PUNCT cana-3678 120 26 and and CCONJ cana-3678 120 27 representation representation NOUN cana-3678 120 28 learning learning NOUN cana-3678 120 29 . . PUNCT cana-3678 121 1 2.1 2.1 NUM cana-3678 121 2 features feature NOUN cana-3678 121 3 of of ADP cana-3678 121 4 fcnn fcnn NOUN cana-3678 121 5 : : PUNCT cana-3678 121 6 universal universal ADJ cana-3678 121 7 approximation approximation NOUN cana-3678 121 8 : : PUNCT cana-3678 121 9 fcnns fcnn NOUN cana-3678 121 10 can can AUX cana-3678 121 11 approximate approximate VERB cana-3678 121 12 any any DET cana-3678 121 13 continuous continuous ADJ cana-3678 121 14 function function NOUN cana-3678 121 15 , , PUNCT cana-3678 121 16 with with ADP cana-3678 121 17 enough enough ADJ cana-3678 121 18 neurons neuron NOUN cana-3678 121 19 and and CCONJ cana-3678 121 20 layers layer NOUN cana-3678 121 21 . . PUNCT cana-3678 122 1 this this DET cana-3678 122 2 characteristic characteristic NOUN cana-3678 122 3 makes make VERB cana-3678 122 4 them they PRON cana-3678 122 5 strong strong ADJ cana-3678 122 6 for for ADP cana-3678 122 7 a a DET cana-3678 122 8 wide wide ADJ cana-3678 122 9 variety variety NOUN cana-3678 122 10 of of ADP cana-3678 122 11 tasks task NOUN cana-3678 122 12 where where SCONJ cana-3678 122 13 complex complex ADJ cana-3678 122 14 relationships relationship NOUN cana-3678 122 15 exist exist VERB cana-3678 122 16 between between ADP cana-3678 122 17 inputs input NOUN cana-3678 122 18 and and CCONJ cana-3678 122 19 outputs output NOUN cana-3678 122 20 . . PUNCT cana-3678 123 1 fcnn fcnn PROPN cana-3678 123 2 features feature VERB cana-3678 123 3 fully fully ADV cana-3678 123 4 connected connected ADJ cana-3678 123 5 layers layer NOUN cana-3678 123 6 , , PUNCT cana-3678 123 7 where where SCONJ cana-3678 123 8 every every DET cana-3678 123 9 neuron neuron NOUN cana-3678 123 10 in in ADP cana-3678 123 11 one one NUM cana-3678 123 12 layer layer NOUN cana-3678 123 13 connects connect VERB cana-3678 123 14 to to ADP cana-3678 123 15 all all DET cana-3678 123 16 neurons neuron NOUN cana-3678 123 17 in in ADP cana-3678 123 18 the the DET cana-3678 123 19 subsequent subsequent ADJ cana-3678 123 20 layers layer NOUN cana-3678 123 21 . . PUNCT cana-3678 124 1 this this PRON cana-3678 124 2 makes make VERB cana-3678 124 3 it it PRON cana-3678 124 4 β€œ " PUNCT cana-3678 124 5 fully fully ADV cana-3678 124 6 connected connect VERB cana-3678 124 7 ” " PUNCT cana-3678 124 8 . . PUNCT cana-3678 125 1 in in ADP cana-3678 125 2 tensorflow tensorflow NOUN cana-3678 125 3 / / SYM cana-3678 125 4 keras keras PROPN cana-3678 125 5 dense dense ADJ cana-3678 125 6 layers layer NOUN cana-3678 125 7 reflects reflect VERB cana-3678 125 8 these these DET cana-3678 125 9 layers layer NOUN cana-3678 125 10 . . PUNCT cana-3678 126 1 typically typically ADV cana-3678 126 2 , , PUNCT cana-3678 126 3 each each DET cana-3678 126 4 layer layer NOUN cana-3678 126 5 incorporates incorporate VERB cana-3678 126 6 an an DET cana-3678 126 7 activation activation NOUN cana-3678 126 8 such such ADJ cana-3678 126 9 as as ADP cana-3678 126 10 relu relu NOUN cana-3678 126 11 , , PUNCT cana-3678 126 12 sigmoid sigmoid NOUN cana-3678 126 13 or or CCONJ cana-3678 126 14 tanh tanh NOUN cana-3678 126 15 that that PRON cana-3678 126 16 introduces introduce VERB cana-3678 126 17 nonlinearity nonlinearity NOUN cana-3678 126 18 , , PUNCT cana-3678 126 19 following follow VERB cana-3678 126 20 the the DET cana-3678 126 21 network network NOUN cana-3678 126 22 to to PART cana-3678 126 23 understand understand VERB cana-3678 126 24 complex complex ADJ cana-3678 126 25 patterns pattern NOUN cana-3678 126 26 . . PUNCT cana-3678 127 1 fcnn fcnn PROPN cana-3678 127 2 lacks lack VERB cana-3678 127 3 any any DET cana-3678 127 4 convolutional convolutional ADJ cana-3678 127 5 or or CCONJ cana-3678 127 6 pooling pool VERB cana-3678 127 7 layers layer NOUN cana-3678 127 8 . . PUNCT cana-3678 128 1 the the DET cana-3678 128 2 input input NOUN cana-3678 128 3 data datum NOUN cana-3678 128 4 is be AUX cana-3678 128 5 considered consider VERB cana-3678 128 6 a a DET cana-3678 128 7 single single ADJ cana-3678 128 8 flat flat ADJ cana-3678 128 9 vector vector NOUN cana-3678 128 10 rather rather ADV cana-3678 128 11 than than ADP cana-3678 128 12 a a DET cana-3678 128 13 spatial spatial ADJ cana-3678 128 14 configuration configuration NOUN cana-3678 128 15 ( ( PUNCT cana-3678 128 16 such such ADJ cana-3678 128 17 as as ADP cana-3678 128 18 image image NOUN cana-3678 128 19 data datum NOUN cana-3678 128 20 ) ) PUNCT cana-3678 128 21 . . PUNCT cana-3678 129 1 the the DET cana-3678 129 2 information information NOUN cana-3678 129 3 moves move VERB cana-3678 129 4 through through ADP cana-3678 129 5 multiple multiple ADJ cana-3678 129 6 fully fully ADV cana-3678 129 7 connected connected ADJ cana-3678 129 8 layers layer NOUN cana-3678 129 9 , , PUNCT cana-3678 129 10 where where SCONJ cana-3678 129 11 each each DET cana-3678 129 12 layer layer NOUN cana-3678 129 13 applies apply VERB cana-3678 129 14 transformations transformation NOUN cana-3678 129 15 as as ADV cana-3678 129 16 well well ADV cana-3678 129 17 as as ADP cana-3678 129 18 activation activation NOUN cana-3678 129 19 functions function NOUN cana-3678 129 20 to to ADP cana-3678 129 21 the the DET cana-3678 129 22 input input NOUN cana-3678 129 23 . . PUNCT cana-3678 130 1 2.2 2.2 NUM cana-3678 130 2 mathematical mathematical ADJ cana-3678 130 3 steps step NOUN cana-3678 130 4 in in ADP cana-3678 130 5 fcnn fcnn NOUN cana-3678 130 6 : : PUNCT cana-3678 130 7 input input NOUN cana-3678 130 8 vectors vector NOUN cana-3678 130 9 can can AUX cana-3678 130 10 be be AUX cana-3678 130 11 represented represent VERB cana-3678 130 12 as as ADP cana-3678 130 13 1 1 NUM cana-3678 130 14 - - PUNCT cana-3678 130 15 dimensional dimensional ADJ cana-3678 130 16 vector vector NOUN cana-3678 130 17 . . PUNCT cana-3678 131 1 here here ADV cana-3678 131 2 𝑆 𝑆 PROPN cana-3678 131 3 = = SYM cana-3678 131 4 ( ( PUNCT cana-3678 131 5 𝑠1 𝑠1 PROPN cana-3678 131 6 , , PUNCT cana-3678 131 7 𝑠2 𝑠2 PROPN cana-3678 131 8 , , PUNCT cana-3678 131 9 … … PUNCT cana-3678 131 10 , , PUNCT cana-3678 131 11 𝑠𝑛 𝑠𝑛 NOUN cana-3678 131 12 ) ) PUNCT cana-3678 131 13 and and CCONJ cana-3678 131 14 𝑑 𝑑 X cana-3678 131 15 = = SYM cana-3678 131 16 ( ( PUNCT cana-3678 131 17 𝑑1 𝑑1 NOUN cana-3678 131 18 , , PUNCT cana-3678 131 19 𝑑2 𝑑2 PROPN cana-3678 131 20 , , PUNCT cana-3678 131 21 … … PUNCT cana-3678 131 22 , , PUNCT cana-3678 131 23 𝑑𝑛 𝑑𝑛 NUM cana-3678 131 24 ) ) PUNCT cana-3678 131 25 . . PUNCT cana-3678 132 1 the the DET cana-3678 132 2 fundamental fundamental ADJ cana-3678 132 3 mathematical mathematical ADJ cana-3678 132 4 procedure procedure NOUN cana-3678 132 5 in in ADP cana-3678 132 6 fcnn fcnn NOUN cana-3678 132 7 involves involve VERB cana-3678 132 8 matrix matrix NOUN cana-3678 132 9 multiplication multiplication NOUN cana-3678 132 10 , , PUNCT cana-3678 132 11 succeeded succeed VERB cana-3678 132 12 by by ADP cana-3678 132 13 activation activation NOUN cana-3678 132 14 functions function NOUN cana-3678 132 15 in in ADP cana-3678 132 16 hidden hidden ADJ cana-3678 132 17 layers layer NOUN cana-3678 132 18 . . PUNCT cana-3678 133 1 compute compute VERB cana-3678 133 2 the the DET cana-3678 133 3 intermediate intermediate ADJ cana-3678 133 4 representation representation NOUN cana-3678 133 5 𝐻(𝑖 𝐻(𝑖 ADP cana-3678 133 6 ) ) PUNCT cana-3678 133 7 = = SYM cana-3678 133 8 𝜎(𝑖)[π‘Š(𝑖)𝑆 𝜎(𝑖)[π‘Š(𝑖)𝑆 PROPN cana-3678 133 9 + + CCONJ cana-3678 133 10 𝑏(𝑖 𝑏(𝑖 PROPN cana-3678 133 11 ) ) PUNCT cana-3678 133 12 ] ] PUNCT cana-3678 134 1 𝐻(𝑖 𝐻(𝑖 VERB cana-3678 134 2 ) ) PUNCT cana-3678 134 3 is be AUX cana-3678 134 4 the the DET cana-3678 134 5 output output NOUN cana-3678 134 6 of of ADP cana-3678 134 7 ith ith ADJ cana-3678 134 8 hidden hide VERB cana-3678 134 9 layer layer NOUN cana-3678 134 10 , , PUNCT cana-3678 134 11 𝜎(𝑖 𝜎(𝑖 NOUN cana-3678 134 12 ) ) PUNCT cana-3678 134 13 = = NOUN cana-3678 134 14 activation activation NOUN cana-3678 134 15 function function NOUN cana-3678 134 16 of of ADP cana-3678 134 17 ith ith PROPN cana-3678 134 18 layer layer NOUN cana-3678 134 19 , , PUNCT cana-3678 134 20 π‘Š(𝑖 π‘Š(𝑖 NOUN cana-3678 134 21 ) ) PUNCT cana-3678 134 22 = = SYM cana-3678 134 23 weight weight NOUN cana-3678 134 24 matrix matrix NOUN cana-3678 134 25 of of ADP cana-3678 134 26 ith ith PROPN cana-3678 134 27 layer layer NOUN cana-3678 134 28 and and CCONJ cana-3678 134 29 𝑏(𝑖 𝑏(𝑖 PROPN cana-3678 134 30 ) ) PUNCT cana-3678 134 31 is be AUX cana-3678 134 32 a a DET cana-3678 134 33 bias bias NOUN cana-3678 134 34 vector vector NOUN cana-3678 134 35 of of ADP cana-3678 134 36 ith ith PROPN cana-3678 134 37 layer layer NOUN cana-3678 134 38 . . PUNCT cana-3678 135 1 compute compute VERB cana-3678 135 2 the the DET cana-3678 135 3 output output NOUN cana-3678 135 4 𝑂 𝑂 NOUN cana-3678 135 5 = = PUNCT cana-3678 135 6 𝐻(𝑖 𝐻(𝑖 ADJ cana-3678 135 7 ) ) PUNCT cana-3678 135 8 = = SYM cana-3678 136 1 𝜎(𝑖)[π‘Š(𝑖)𝐻(𝑖 𝜎(𝑖)[π‘Š(𝑖)𝐻(𝑖 ADJ cana-3678 136 2 βˆ’ βˆ’ NOUN cana-3678 136 3 1 1 NUM cana-3678 136 4 ) ) PUNCT cana-3678 136 5 + + NUM cana-3678 136 6 𝑏(𝑖 𝑏(𝑖 NOUN cana-3678 136 7 ) ) PUNCT cana-3678 136 8 ] ] PUNCT cana-3678 136 9 now now ADV cana-3678 136 10 concept concept NOUN cana-3678 136 11 of of ADP cana-3678 136 12 backpropagation backpropagation NOUN cana-3678 136 13 is be AUX cana-3678 136 14 used use VERB cana-3678 136 15 . . PUNCT cana-3678 137 1 first first ADJ cana-3678 137 2 loss loss NOUN cana-3678 137 3 is be AUX cana-3678 137 4 calculated calculate VERB cana-3678 137 5 based base VERB cana-3678 137 6 on on ADP cana-3678 137 7 true true ADJ cana-3678 137 8 value value NOUN cana-3678 137 9 and and CCONJ cana-3678 137 10 predicted predict VERB cana-3678 137 11 value value NOUN cana-3678 137 12 . . PUNCT cana-3678 138 1 then then ADV cana-3678 138 2 gradient gradient NOUN cana-3678 138 3 of of ADP cana-3678 138 4 loss loss NOUN cana-3678 138 5 function function NOUN cana-3678 138 6 with with ADP cana-3678 138 7 respect respect NOUN cana-3678 138 8 to to ADP cana-3678 138 9 π‘Š π‘Š PROPN cana-3678 138 10 is be AUX cana-3678 138 11 calculated calculate VERB cana-3678 138 12 . . PUNCT cana-3678 139 1 then then ADV cana-3678 139 2 algorithm algorithm PROPN cana-3678 139 3 modifies modify VERB cana-3678 139 4 weight weight NOUN cana-3678 139 5 w w PROPN cana-3678 139 6 and and CCONJ cana-3678 139 7 biases bias NOUN cana-3678 139 8 b b X cana-3678 139 9 by by ADP cana-3678 139 10 applying apply VERB cana-3678 139 11 gradients gradient NOUN cana-3678 139 12 to to PART cana-3678 139 13 reduce reduce VERB cana-3678 139 14 the the DET cana-3678 139 15 loss loss NOUN cana-3678 139 16 function function NOUN cana-3678 139 17 l. l. NOUN cana-3678 139 18 a a DET cana-3678 139 19 loss loss NOUN cana-3678 139 20 function function NOUN cana-3678 139 21 is be AUX cana-3678 139 22 also also ADV cana-3678 139 23 known know VERB cana-3678 139 24 as as ADP cana-3678 139 25 cost cost NOUN cana-3678 139 26 function function NOUN cana-3678 139 27 is be AUX cana-3678 139 28 a a DET cana-3678 139 29 mathematical mathematical ADJ cana-3678 139 30 function function NOUN cana-3678 139 31 that that PRON cana-3678 139 32 quantifies quantify VERB cana-3678 139 33 the the DET cana-3678 139 34 cost cost NOUN cana-3678 139 35 or or CCONJ cana-3678 139 36 error error NOUN cana-3678 139 37 associated associate VERB cana-3678 139 38 with with ADP cana-3678 139 39 a a DET cana-3678 139 40 set set NOUN cana-3678 139 41 of of ADP cana-3678 139 42 data datum NOUN cana-3678 139 43 points point NOUN cana-3678 139 44 . . PUNCT cana-3678 140 1 π‘Š π‘Š NOUN cana-3678 140 2 ← ← NOUN cana-3678 140 3 π‘Š π‘Š PROPN cana-3678 140 4 βˆ’ βˆ’ PROPN cana-3678 140 5 Ξ· Ξ· PROPN cana-3678 140 6 βˆ‚πΏ βˆ‚πΏ PROPN cana-3678 140 7 βˆ‚π‘Š βˆ‚π‘Š ADP cana-3678 140 8 . . PUNCT cana-3678 141 1 here here ADV cana-3678 141 2 πœ‚ πœ‚ NOUN cana-3678 141 3 is be AUX cana-3678 141 4 a a DET cana-3678 141 5 learning learning NOUN cana-3678 141 6 rate rate NOUN cana-3678 141 7 and and CCONJ cana-3678 141 8 πœ•πΏ πœ•πΏ PROPN cana-3678 141 9 πœ•π‘Š πœ•π‘Š PROPN cana-3678 141 10 is be AUX cana-3678 141 11 a a DET cana-3678 141 12 gradient gradient NOUN cana-3678 141 13 of of ADP cana-3678 141 14 the the DET cana-3678 141 15 loss loss NOUN cana-3678 141 16 function function NOUN cana-3678 141 17 with with ADP cana-3678 141 18 respect respect NOUN cana-3678 141 19 to to ADP cana-3678 141 20 π‘Š. π‘Š. PROPN cana-3678 141 21 when when SCONJ cana-3678 141 22 utilizing utilize VERB cana-3678 141 23 fcnns fcnn NOUN cana-3678 141 24 , , PUNCT cana-3678 141 25 it it PRON cana-3678 141 26 may may AUX cana-3678 141 27 be be AUX cana-3678 141 28 necessary necessary ADJ cana-3678 141 29 to to PART cana-3678 141 30 adjust adjust VERB cana-3678 141 31 hyperparameter hyperparameter NOUN cana-3678 141 32 as as ADV cana-3678 141 33 well well ADV cana-3678 141 34 . . PUNCT cana-3678 142 1 number number NOUN cana-3678 142 2 of of ADP cana-3678 142 3 neurons neuron NOUN cana-3678 142 4 in in ADP cana-3678 142 5 each each DET cana-3678 142 6 layer layer NOUN cana-3678 142 7 are be AUX cana-3678 142 8 adjusted adjust VERB cana-3678 142 9 . . PUNCT cana-3678 143 1 adding add VERB cana-3678 143 2 more more ADJ cana-3678 143 3 layers layer NOUN cana-3678 143 4 and and CCONJ cana-3678 143 5 neurons neuron NOUN cana-3678 143 6 enhances enhance VERB cana-3678 143 7 capacity capacity NOUN cana-3678 143 8 but but CCONJ cana-3678 143 9 may may AUX cana-3678 143 10 lead lead VERB cana-3678 143 11 to to ADP cana-3678 143 12 overfitting overfitte VERB cana-3678 143 13 . . PUNCT cana-3678 144 1 learning learn VERB cana-3678 144 2 rate rate NOUN cana-3678 144 3 is be AUX cana-3678 144 4 also also ADV cana-3678 144 5 adjusted adjust VERB cana-3678 144 6 as as SCONJ cana-3678 144 7 it it PRON cana-3678 144 8 affects affect VERB cana-3678 144 9 how how SCONJ cana-3678 144 10 quickly quickly ADV cana-3678 144 11 weights weight NOUN cana-3678 144 12 are be AUX cana-3678 144 13 adjusted adjust VERB cana-3678 144 14 and and CCONJ cana-3678 144 15 algorithm algorithm NOUN cana-3678 144 16 converge converge VERB cana-3678 144 17 fast fast ADV cana-3678 144 18 . . PUNCT cana-3678 145 1 regularization regularization NOUN cana-3678 145 2 governs govern VERB cana-3678 145 3 the the DET cana-3678 145 4 punishment punishment NOUN cana-3678 145 5 imposed impose VERB cana-3678 145 6 on on ADP cana-3678 145 7 substantial substantial ADJ cana-3678 145 8 weights weight NOUN cana-3678 145 9 to to PART cana-3678 145 10 avoid avoid VERB cana-3678 145 11 overfitting overfitte VERB cana-3678 145 12 . . PUNCT cana-3678 146 1 l2 l2 NOUN cana-3678 146 2 regularization regularization NOUN cana-3678 146 3 ( ( PUNCT cana-3678 146 4 ridge ridge NOUN cana-3678 146 5 regularization regularization NOUN cana-3678 146 6 ) ) PUNCT cana-3678 146 7 is be AUX cana-3678 146 8 applied apply VERB cana-3678 146 9 here here ADV cana-3678 146 10 . . PUNCT cana-3678 147 1 π‘™π‘œπ‘ π‘  π‘™π‘œπ‘ π‘  NOUN cana-3678 147 2 = = SYM cana-3678 147 3 π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ NOUN cana-3678 147 4 π‘™π‘œπ‘ π‘  π‘™π‘œπ‘ π‘  NOUN cana-3678 147 5 + + CCONJ cana-3678 147 6 πœ† πœ† DET cana-3678 147 7 ||πœƒ(π‘Š ||πœƒ(π‘Š NOUN cana-3678 147 8 , , PUNCT cana-3678 147 9 𝑏)|| 𝑏)|| NUM cana-3678 147 10 2 2 NUM cana-3678 147 11 , , PUNCT cana-3678 147 12 where where SCONJ cana-3678 147 13 πœ† πœ† NOUN cana-3678 147 14 regulates regulate VERB cana-3678 147 15 the the DET cana-3678 147 16 significance significance NOUN cana-3678 147 17 of of ADP cana-3678 147 18 regularization regularization NOUN cana-3678 147 19 . . PUNCT cana-3678 148 1 communications communication NOUN cana-3678 148 2 on on ADP cana-3678 148 3 applied apply VERB cana-3678 148 4 nonlinear nonlinear ADJ cana-3678 148 5 analysis analysis NOUN cana-3678 148 6 issn issn NOUN cana-3678 148 7 : : PUNCT cana-3678 148 8 1074 1074 NUM cana-3678 148 9 - - PUNCT cana-3678 148 10 133x 133x NUM cana-3678 148 11 vol vol NOUN cana-3678 148 12 32 32 NUM cana-3678 148 13 no no NOUN cana-3678 148 14 . . PUNCT cana-3678 149 1 8s 8s PROPN cana-3678 149 2 ( ( PUNCT cana-3678 149 3 2025 2025 NUM cana-3678 149 4 ) ) PUNCT cana-3678 149 5 325 325 NUM cana-3678 149 6 https://internationalpubls.com https://internationalpubls.com X cana-3678 149 7 data datum NOUN cana-3678 149 8 is be AUX cana-3678 149 9 imported import VERB cana-3678 149 10 in in ADP cana-3678 149 11 batch batch NOUN cana-3678 149 12 . . PUNCT cana-3678 150 1 incorporate incorporate VERB cana-3678 150 2 batch batch NOUN cana-3678 150 3 normalization normalization NOUN cana-3678 150 4 to to PART cana-3678 150 5 enhance enhance VERB cana-3678 150 6 training training NOUN cana-3678 150 7 stability stability NOUN cana-3678 150 8 and and CCONJ cana-3678 150 9 accelerate accelerate VERB cana-3678 150 10 the the DET cana-3678 150 11 process process NOUN cana-3678 150 12 . . PUNCT cana-3678 151 1 generally generally ADV cana-3678 151 2 adaptive adaptive ADJ cana-3678 151 3 optimizers optimizer NOUN cana-3678 151 4 like like ADP cana-3678 151 5 adam adam NOUN cana-3678 151 6 and and CCONJ cana-3678 151 7 rmsprop rmsprop NOUN cana-3678 151 8 for for ADP cana-3678 151 9 better well ADJ cana-3678 151 10 convergence convergence NOUN cana-3678 151 11 are be AUX cana-3678 151 12 used use VERB cana-3678 151 13 in in ADP cana-3678 151 14 fcnn fcnn ADJ cana-3678 151 15 . . PUNCT cana-3678 152 1 4 4 X cana-3678 152 2 . . NOUN cana-3678 152 3 results result VERB cana-3678 152 4 the the DET cana-3678 152 5 mentioned mention VERB cana-3678 152 6 above above ADP cana-3678 152 7 nonlinear nonlinear ADJ cana-3678 152 8 model model NOUN cana-3678 152 9 is be AUX cana-3678 152 10 computed compute VERB cana-3678 152 11 for for ADP cana-3678 152 12 risk risk NOUN cana-3678 152 13 - - PUNCT cana-3678 152 14 free free ADJ cana-3678 152 15 interest interest NOUN cana-3678 152 16 rate rate NOUN cana-3678 152 17 r r NOUN cana-3678 152 18 = = NOUN cana-3678 152 19 0.05 0.05 NUM cana-3678 152 20 , , PUNCT cana-3678 153 1 volatility volatility NOUN cana-3678 153 2 𝜎 𝜎 NOUN cana-3678 153 3 = = SYM cana-3678 153 4 0.3 0.3 NUM cana-3678 153 5 , , PUNCT cana-3678 153 6 strike strike VERB cana-3678 153 7 price price NOUN cana-3678 153 8 k k NOUN cana-3678 153 9 = = SYM cana-3678 153 10 40 40 NUM cana-3678 153 11 , , PUNCT cana-3678 153 12 smax smax PROPN cana-3678 153 13 = = SYM cana-3678 153 14 70 70 NUM cana-3678 153 15 , , PUNCT cana-3678 153 16 proportional proportional ADJ cana-3678 153 17 transaction transaction NOUN cana-3678 153 18 cost cost VERB cana-3678 153 19 q q NOUN cana-3678 153 20 = = NOUN cana-3678 153 21 0.01 0.01 NUM cana-3678 153 22 and and CCONJ cana-3678 153 23 time time NOUN cana-3678 153 24 of of ADP cana-3678 153 25 maturity maturity NOUN cana-3678 153 26 t t NOUN cana-3678 153 27 = = SYM cana-3678 153 28 1 1 NUM cana-3678 153 29 year year NOUN cana-3678 153 30 . . PUNCT cana-3678 154 1 πœ— πœ— NOUN cana-3678 154 2 illiquid illiquid ADJ cana-3678 154 3 parameter parameter NOUN cana-3678 154 4 takes take VERB cana-3678 154 5 the the DET cana-3678 154 6 value value NOUN cana-3678 154 7 in in ADP cana-3678 154 8 a a DET cana-3678 154 9 range range NOUN cana-3678 154 10 of of ADP cana-3678 154 11 0 0 NUM cana-3678 154 12 to to ADP cana-3678 154 13 0.03 0.03 NUM cana-3678 154 14 . . PUNCT cana-3678 155 1 for for ADP cana-3678 155 2 hyperparameter hyperparameter NOUN cana-3678 155 3 setting set VERB cana-3678 155 4 , , PUNCT cana-3678 155 5 in in ADP cana-3678 155 6 each each DET cana-3678 155 7 layer layer NOUN cana-3678 155 8 different different ADJ cana-3678 155 9 number number NOUN cana-3678 155 10 of of ADP cana-3678 155 11 neurons neuron NOUN cana-3678 155 12 are be AUX cana-3678 155 13 taken take VERB cana-3678 155 14 for for ADP cana-3678 155 15 number number NOUN cana-3678 155 16 of of ADP cana-3678 155 17 hidden hide VERB cana-3678 155 18 layers layer NOUN cana-3678 155 19 = = SYM cana-3678 155 20 6 6 X cana-3678 155 21 . . X cana-3678 155 22 l2 l2 NOUN cana-3678 155 23 regularization regularization NOUN cana-3678 155 24 with with ADP cana-3678 155 25 learning learn VERB cana-3678 155 26 rate rate NOUN cana-3678 155 27 πœ‚ πœ‚ NOUN cana-3678 155 28 = = SYM cana-3678 155 29 0.001 0.001 NUM cana-3678 155 30 is be AUX cana-3678 155 31 applied apply VERB cana-3678 155 32 . . PUNCT cana-3678 156 1 adam adam PROPN cana-3678 156 2 optimizer optimizer NOUN cana-3678 156 3 is be AUX cana-3678 156 4 used use VERB cana-3678 156 5 with with ADP cana-3678 156 6 batch batch NOUN cana-3678 156 7 size size NOUN cana-3678 156 8 16 16 NUM cana-3678 156 9 . . PUNCT cana-3678 157 1 exponential exponential ADJ cana-3678 157 2 linear linear PROPN cana-3678 157 3 unit unit NOUN cana-3678 157 4 ( ( PUNCT cana-3678 157 5 elu elu NOUN cana-3678 157 6 ) ) PUNCT cana-3678 157 7 activation activation NOUN cana-3678 157 8 function function NOUN cana-3678 157 9 is be AUX cana-3678 157 10 used use VERB cana-3678 157 11 in in ADP cana-3678 157 12 hidden hide VERB cana-3678 157 13 layers layer NOUN cana-3678 157 14 and and CCONJ cana-3678 157 15 linear linear ADJ cana-3678 157 16 function function NOUN cana-3678 157 17 as as SCONJ cana-3678 157 18 an an DET cana-3678 157 19 activation activation NOUN cana-3678 157 20 is be AUX cana-3678 157 21 used use VERB cana-3678 157 22 in in ADP cana-3678 157 23 output output NOUN cana-3678 157 24 layer layer NOUN cana-3678 157 25 . . PUNCT cana-3678 158 1 here here ADV cana-3678 158 2 , , PUNCT cana-3678 158 3 loss loss NOUN cana-3678 158 4 function function NOUN cana-3678 158 5 is be AUX cana-3678 158 6 defined define VERB cana-3678 158 7 with with ADP cana-3678 158 8 a a DET cana-3678 158 9 custom custom NOUN cana-3678 158 10 term term NOUN cana-3678 158 11 that that PRON cana-3678 158 12 is be AUX cana-3678 158 13 transaction transaction NOUN cana-3678 158 14 costs cost NOUN cana-3678 158 15 . . PUNCT cana-3678 159 1 mathematically mathematically ADV cana-3678 159 2 , , PUNCT cana-3678 159 3 π‘™π‘œπ‘ π‘  π‘™π‘œπ‘ π‘  NOUN cana-3678 159 4 = = SYM cana-3678 159 5 ( ( PUNCT cana-3678 159 6 πΆπ‘‘π‘Ÿπ‘’π‘’ πΆπ‘‘π‘Ÿπ‘’π‘’ PROPN cana-3678 159 7 βˆ’ βˆ’ PROPN cana-3678 160 1 πΆπ‘π‘Ÿπ‘’π‘‘π‘–π‘π‘‘π‘’π‘‘ πΆπ‘π‘Ÿπ‘’π‘‘π‘–π‘π‘‘π‘’π‘‘ PROPN cana-3678 160 2 ) ) PUNCT cana-3678 160 3 2 2 NUM cana-3678 160 4 + + NOUN cana-3678 160 5 transaction transaction NOUN cana-3678 160 6 costs cost NOUN cana-3678 160 7 table table NOUN cana-3678 160 8 1 1 NUM cana-3678 160 9 illustrates illustrate VERB cana-3678 160 10 for for ADP cana-3678 160 11 loss loss NOUN cana-3678 160 12 function function NOUN cana-3678 160 13 defined define VERB cana-3678 160 14 by by ADP cana-3678 160 15 mean mean ADJ cana-3678 160 16 squared square VERB cana-3678 160 17 error error NOUN cana-3678 160 18 ( ( PUNCT cana-3678 160 19 mse mse NOUN cana-3678 160 20 ) ) PUNCT cana-3678 160 21 . . PUNCT cana-3678 161 1 it it PRON cana-3678 161 2 shows show VERB cana-3678 161 3 that that SCONJ cana-3678 161 4 as as SCONJ cana-3678 161 5 the the DET cana-3678 161 6 number number NOUN cana-3678 161 7 of of ADP cana-3678 161 8 neurons neuron NOUN cana-3678 161 9 changes change VERB cana-3678 161 10 the the DET cana-3678 161 11 accuracy accuracy NOUN cana-3678 161 12 changes change NOUN cana-3678 161 13 . . PUNCT cana-3678 162 1 it it PRON cana-3678 162 2 shows show VERB cana-3678 162 3 best well ADV cana-3678 162 4 predicted predict VERB cana-3678 162 5 call call NOUN cana-3678 162 6 option option NOUN cana-3678 162 7 value value NOUN cana-3678 162 8 for for ADP cana-3678 162 9 200 200 NUM cana-3678 162 10 number number NOUN cana-3678 162 11 of of ADP cana-3678 162 12 neurons neuron NOUN cana-3678 162 13 . . PUNCT cana-3678 163 1 table:1 table:1 NOUN cana-3678 163 2 s s PRON cana-3678 163 3 c_target c_target NOUN cana-3678 163 4 no no INTJ cana-3678 163 5 . . PUNCT cana-3678 163 6 of of ADP cana-3678 163 7 neurons neuron NOUN cana-3678 163 8 64 64 NUM cana-3678 163 9 100 100 NUM cana-3678 163 10 200 200 NUM cana-3678 163 11 c_predicted c_predicte VERB cana-3678 163 12 40.6 40.6 NUM cana-3678 163 13 0.6 0.6 NUM cana-3678 163 14 0.79160 0.79160 NUM cana-3678 163 15 0.70215 0.70215 NUM cana-3678 164 1 0.76630 0.76630 NUM cana-3678 164 2 49 49 NUM cana-3678 164 3 9.0 9.0 NUM cana-3678 164 4 8.98727 8.98727 NUM cana-3678 164 5 8.93354 8.93354 NUM cana-3678 164 6 9.00123 9.00123 NUM cana-3678 164 7 56 56 NUM cana-3678 164 8 16.0 16.0 NUM cana-3678 164 9 15.99862 15.99862 NUM cana-3678 164 10 15.97565 15.97565 NUM cana-3678 164 11 16.04225 16.04225 NUM cana-3678 164 12 63 63 NUM cana-3678 164 13 23.0 23.0 NUM cana-3678 164 14 22.98522 22.98522 NUM cana-3678 164 15 22.99294 22.99294 NUM cana-3678 164 16 23.04190 23.04190 NUM cana-3678 164 17 67.2 67.2 NUM cana-3678 164 18 27.2 27.2 NUM cana-3678 164 19 27.15376 27.15376 NUM cana-3678 164 20 27.17203 27.17203 NUM cana-3678 164 21 27.22907 27.22907 NUM cana-3678 164 22 figure figure NOUN cana-3678 164 23 1 1 NUM cana-3678 164 24 represents represent VERB cana-3678 164 25 the the DET cana-3678 164 26 graphs graph NOUN cana-3678 164 27 of of ADP cana-3678 164 28 number number NOUN cana-3678 164 29 of of ADP cana-3678 164 30 neurons neuron NOUN cana-3678 164 31 in in ADP cana-3678 164 32 hidden hidden ADJ cana-3678 164 33 layers layer NOUN cana-3678 164 34 verses verses ADP cana-3678 164 35 loss loss NOUN cana-3678 164 36 . . PUNCT cana-3678 165 1 it it PRON cana-3678 165 2 shows show VERB cana-3678 165 3 the the DET cana-3678 165 4 best good ADJ cana-3678 165 5 result result NOUN cana-3678 165 6 for for ADP cana-3678 165 7 200 200 NUM cana-3678 165 8 number number NOUN cana-3678 165 9 of of ADP cana-3678 165 10 neurons neuron NOUN cana-3678 165 11 . . PUNCT cana-3678 166 1 figure figure NOUN cana-3678 166 2 1 1 NUM cana-3678 166 3 ( ( PUNCT cana-3678 166 4 a)no a)no NOUN cana-3678 166 5 . . NOUN cana-3678 166 6 of of ADP cana-3678 166 7 neurons neuron NOUN cana-3678 166 8 = = SYM cana-3678 166 9 64 64 NUM cana-3678 166 10 ( ( PUNCT cana-3678 166 11 b b NOUN cana-3678 166 12 ) ) PUNCT cana-3678 166 13 no no NOUN cana-3678 166 14 . . NOUN cana-3678 167 1 of of ADP cana-3678 167 2 neurons neuron NOUN cana-3678 167 3 = = SYM cana-3678 167 4 100 100 NUM cana-3678 167 5 ( ( PUNCT cana-3678 167 6 c c NOUN cana-3678 167 7 ) ) PUNCT cana-3678 167 8 no no NOUN cana-3678 167 9 . . NOUN cana-3678 168 1 of of ADP cana-3678 168 2 neurons neuron NOUN cana-3678 168 3 = = NOUN cana-3678 168 4 200 200 NUM cana-3678 168 5 figure figure NOUN cana-3678 168 6 2 2 NUM cana-3678 168 7 shows show VERB cana-3678 168 8 the the DET cana-3678 168 9 behaviour behaviour NOUN cana-3678 168 10 of of ADP cana-3678 168 11 loss loss NOUN cana-3678 168 12 function function NOUN cana-3678 168 13 evaluated evaluate VERB cana-3678 168 14 by by ADP cana-3678 168 15 mean mean ADJ cana-3678 168 16 absolute absolute ADJ cana-3678 168 17 error error NOUN cana-3678 168 18 ( ( PUNCT cana-3678 168 19 mae mae PROPN cana-3678 168 20 ) ) PUNCT cana-3678 168 21 . . PUNCT cana-3678 169 1 communications communication NOUN cana-3678 169 2 on on ADP cana-3678 169 3 applied apply VERB cana-3678 169 4 nonlinear nonlinear ADJ cana-3678 169 5 analysis analysis NOUN cana-3678 169 6 issn issn NOUN cana-3678 169 7 : : PUNCT cana-3678 169 8 1074 1074 NUM cana-3678 169 9 - - PUNCT cana-3678 169 10 133x 133x NUM cana-3678 169 11 vol vol NOUN cana-3678 169 12 32 32 NUM cana-3678 169 13 no no NOUN cana-3678 169 14 . . PUNCT cana-3678 170 1 8s 8s PROPN cana-3678 170 2 ( ( PUNCT cana-3678 170 3 2025 2025 NUM cana-3678 170 4 ) ) PUNCT cana-3678 170 5 326 326 NUM cana-3678 170 6 https://internationalpubls.com https://internationalpubls.com X cana-3678 170 7 figure figure NOUN cana-3678 170 8 2 2 NUM cana-3678 170 9 ( ( PUNCT cana-3678 170 10 a)no a)no NOUN cana-3678 170 11 . . NOUN cana-3678 170 12 of of ADP cana-3678 170 13 neurons neuron NOUN cana-3678 170 14 = = SYM cana-3678 170 15 64 64 NUM cana-3678 170 16 ( ( PUNCT cana-3678 170 17 b b NOUN cana-3678 170 18 ) ) PUNCT cana-3678 170 19 no no NOUN cana-3678 170 20 . . NOUN cana-3678 170 21 of of ADP cana-3678 170 22 neurons neuron NOUN cana-3678 170 23 = = SYM cana-3678 170 24 100 100 NUM cana-3678 170 25 ( ( PUNCT cana-3678 170 26 c c NOUN cana-3678 170 27 ) ) PUNCT cana-3678 170 28 no no NOUN cana-3678 170 29 . . NOUN cana-3678 170 30 of of ADP cana-3678 170 31 neurons neuron NOUN cana-3678 170 32 = = NOUN cana-3678 170 33 200 200 NUM cana-3678 170 34 figure figure NOUN cana-3678 170 35 1 1 NUM cana-3678 170 36 and and CCONJ cana-3678 170 37 figure figure VERB cana-3678 170 38 2 2 NUM cana-3678 170 39 indicate indicate VERB cana-3678 170 40 that that SCONJ cana-3678 170 41 the the DET cana-3678 170 42 loss loss NOUN cana-3678 170 43 function function NOUN cana-3678 170 44 computed compute VERB cana-3678 170 45 with with ADP cana-3678 170 46 mse mse NOUN cana-3678 170 47 outperforms outperform VERB cana-3678 170 48 the the DET cana-3678 170 49 one one NOUN cana-3678 170 50 calculated calculate VERB cana-3678 170 51 with with ADP cana-3678 170 52 mae mae PROPN cana-3678 170 53 . . PROPN cana-3678 171 1 both both DET cana-3678 171 2 loss loss NOUN cana-3678 171 3 functions function NOUN cana-3678 171 4 show show VERB cana-3678 171 5 best good ADJ cana-3678 171 6 result result NOUN cana-3678 171 7 for for ADP cana-3678 171 8 200 200 NUM cana-3678 171 9 number number NOUN cana-3678 171 10 of of ADP cana-3678 171 11 neurons neuron NOUN cana-3678 171 12 in in ADP cana-3678 171 13 hidden hidden ADJ cana-3678 171 14 layers layer NOUN cana-3678 171 15 , , PUNCT cana-3678 171 16 but but CCONJ cana-3678 171 17 mse mse NOUN cana-3678 171 18 achieves achieve VERB cana-3678 171 19 best well ADV cana-3678 171 20 more more ADV cana-3678 171 21 swiftly swiftly ADV cana-3678 171 22 than than ADP cana-3678 171 23 mae mae PROPN cana-3678 171 24 . . PROPN cana-3678 171 25 figure figure NOUN cana-3678 171 26 3 3 NUM cana-3678 171 27 presents present VERB cana-3678 171 28 the the DET cana-3678 171 29 effect effect NOUN cana-3678 171 30 of of ADP cana-3678 171 31 transaction transaction NOUN cana-3678 171 32 costs cost NOUN cana-3678 171 33 and and CCONJ cana-3678 171 34 illiquid illiquid ADJ cana-3678 171 35 market market NOUN cana-3678 171 36 position position NOUN cana-3678 171 37 ( ( PUNCT cana-3678 171 38 liquidity liquidity NOUN cana-3678 171 39 parameter parameter NOUN cana-3678 171 40 ) ) PUNCT cana-3678 171 41 for for ADP cana-3678 171 42 european european ADJ cana-3678 171 43 call call NOUN cana-3678 171 44 option option NOUN cana-3678 171 45 with with ADP cana-3678 171 46 loss loss NOUN cana-3678 171 47 mse mse NOUN cana-3678 171 48 . . PUNCT cana-3678 172 1 it it PRON cana-3678 172 2 indicates indicate VERB cana-3678 172 3 that that SCONJ cana-3678 172 4 as as SCONJ cana-3678 172 5 the the DET cana-3678 172 6 transaction transaction NOUN cana-3678 172 7 costs cost NOUN cana-3678 172 8 and and CCONJ cana-3678 172 9 liquidity liquidity NOUN cana-3678 172 10 parameter parameter NOUN cana-3678 172 11 increase increase NOUN cana-3678 172 12 value value NOUN cana-3678 172 13 of of ADP cana-3678 172 14 the the DET cana-3678 172 15 call call NOUN cana-3678 172 16 option option NOUN cana-3678 172 17 also also ADV cana-3678 172 18 increases increase VERB cana-3678 172 19 . . PUNCT cana-3678 173 1 it it PRON cana-3678 173 2 also also ADV cana-3678 173 3 illustrates illustrate VERB cana-3678 173 4 that that SCONJ cana-3678 173 5 by by ADP cana-3678 173 6 changing change VERB cana-3678 173 7 the the DET cana-3678 173 8 number number NOUN cana-3678 173 9 of of ADP cana-3678 173 10 neurons neuron NOUN cana-3678 173 11 in in ADP cana-3678 173 12 hidden hidden ADJ cana-3678 173 13 layers layer NOUN cana-3678 173 14 , , PUNCT cana-3678 173 15 accuracy accuracy NOUN cana-3678 173 16 at at ADP cana-3678 173 17 jump jump NOUN cana-3678 173 18 point point NOUN cana-3678 173 19 that that PRON cana-3678 173 20 is be AUX cana-3678 173 21 at at ADP cana-3678 173 22 strike strike NOUN cana-3678 173 23 price price NOUN cana-3678 173 24 k=40 k=40 VERB cana-3678 173 25 can can AUX cana-3678 173 26 also also ADV cana-3678 173 27 increase increase VERB cana-3678 173 28 . . PUNCT cana-3678 174 1 ( ( PUNCT cana-3678 174 2 a)no a)no NOUN cana-3678 174 3 . . NOUN cana-3678 174 4 of of ADP cana-3678 174 5 neurons neuron NOUN cana-3678 174 6 = = SYM cana-3678 174 7 64 64 NUM cana-3678 174 8 ( ( PUNCT cana-3678 174 9 b b NOUN cana-3678 174 10 ) ) PUNCT cana-3678 174 11 no no NOUN cana-3678 174 12 . . NOUN cana-3678 174 13 of of ADP cana-3678 174 14 neurons neuron NOUN cana-3678 174 15 = = SYM cana-3678 174 16 100 100 NUM cana-3678 174 17 ( ( PUNCT cana-3678 174 18 c c NOUN cana-3678 174 19 ) ) PUNCT cana-3678 174 20 no no NOUN cana-3678 174 21 . . NOUN cana-3678 174 22 of of ADP cana-3678 174 23 neurons neuron NOUN cana-3678 174 24 = = NOUN cana-3678 174 25 200 200 NUM cana-3678 174 26 figure figure NOUN cana-3678 174 27 3 3 NUM cana-3678 174 28 : : PUNCT cana-3678 174 29 european european ADJ cana-3678 174 30 call call NOUN cana-3678 174 31 option option NOUN cana-3678 174 32 values value NOUN cana-3678 174 33 verses verses ADP cana-3678 174 34 asset asset NOUN cana-3678 174 35 price price NOUN cana-3678 174 36 s s NOUN cana-3678 174 37 for for ADP cana-3678 174 38 strike strike NOUN cana-3678 174 39 price price NOUN cana-3678 174 40 k k NOUN cana-3678 174 41 = = SYM cana-3678 174 42 40 40 NUM cana-3678 174 43 , , PUNCT cana-3678 174 44 volatility volatility NOUN cana-3678 174 45 𝜎 𝜎 NOUN cana-3678 174 46 = = SYM cana-3678 174 47 0.3 0.3 NUM cana-3678 174 48 , , PUNCT cana-3678 174 49 risk risk NOUN cana-3678 174 50 - - PUNCT cana-3678 174 51 free free ADJ cana-3678 174 52 interest interest NOUN cana-3678 174 53 rate rate NOUN cana-3678 174 54 r r NOUN cana-3678 174 55 = = NOUN cana-3678 174 56 0.05 0.05 NUM cana-3678 174 57 , , PUNCT cana-3678 174 58 s_max s_max NOUN cana-3678 174 59 = = SYM cana-3678 174 60 70 70 NUM cana-3678 174 61 , , PUNCT cana-3678 174 62 time time NOUN cana-3678 174 63 to to ADP cana-3678 174 64 maturity maturity NOUN cana-3678 174 65 t t NOUN cana-3678 174 66 = = SYM cana-3678 174 67 1 1 NUM cana-3678 174 68 year year NOUN cana-3678 174 69 . . PUNCT cana-3678 175 1 also also ADV cana-3678 175 2 , , PUNCT cana-3678 175 3 for for ADP cana-3678 175 4 european european ADJ cana-3678 175 5 call call NOUN cana-3678 175 6 options option NOUN cana-3678 175 7 , , PUNCT cana-3678 175 8 the the DET cana-3678 175 9 spatio spatio PROPN cana-3678 175 10 - - PUNCT cana-3678 175 11 temporal temporal ADJ cana-3678 175 12 dynamics dynamic NOUN cana-3678 175 13 is be AUX cana-3678 175 14 presented present VERB cana-3678 175 15 for for ADP cana-3678 175 16 mentioned mention VERB cana-3678 175 17 nonlinear nonlinear ADJ cana-3678 175 18 effects effect NOUN cana-3678 175 19 of of ADP cana-3678 175 20 financial financial ADJ cana-3678 175 21 market market NOUN cana-3678 175 22 in in ADP cana-3678 175 23 figure figure NOUN cana-3678 175 24 4 4 NUM cana-3678 175 25 . . PUNCT cana-3678 176 1 it it PRON cana-3678 176 2 is be AUX cana-3678 176 3 noted note VERB cana-3678 176 4 that that SCONJ cana-3678 176 5 a a DET cana-3678 176 6 rise rise NOUN cana-3678 176 7 in in ADP cana-3678 176 8 the the DET cana-3678 176 9 price price NOUN cana-3678 176 10 of of ADP cana-3678 176 11 transaction transaction NOUN cana-3678 176 12 costs cost NOUN cana-3678 176 13 and and CCONJ cana-3678 176 14 liquidity liquidity NOUN cana-3678 176 15 parameter parameter NOUN cana-3678 176 16 the the DET cana-3678 176 17 underlying underlie VERB cana-3678 176 18 asset asset NOUN cana-3678 176 19 elevates elevate VERB cana-3678 176 20 the the DET cana-3678 176 21 value value NOUN cana-3678 176 22 of of ADP cana-3678 176 23 the the DET cana-3678 176 24 european european ADJ cana-3678 176 25 call call NOUN cana-3678 176 26 option option NOUN cana-3678 176 27 . . PUNCT cana-3678 177 1 figure figure NOUN cana-3678 177 2 4 4 NUM cana-3678 177 3 european european ADJ cana-3678 177 4 call call NOUN cana-3678 177 5 option option NOUN cana-3678 177 6 value value NOUN cana-3678 177 7 communications communication NOUN cana-3678 177 8 on on ADP cana-3678 177 9 applied apply VERB cana-3678 177 10 nonlinear nonlinear ADJ cana-3678 177 11 analysis analysis NOUN cana-3678 177 12 issn issn NOUN cana-3678 177 13 : : PUNCT cana-3678 177 14 1074 1074 NUM cana-3678 177 15 - - PUNCT cana-3678 177 16 133x 133x NUM cana-3678 177 17 vol vol NOUN cana-3678 177 18 32 32 NUM cana-3678 177 19 no no NOUN cana-3678 177 20 . . PUNCT cana-3678 178 1 8s 8s PROPN cana-3678 178 2 ( ( PUNCT cana-3678 178 3 2025 2025 NUM cana-3678 178 4 ) ) PUNCT cana-3678 178 5 327 327 NUM cana-3678 178 6 https://internationalpubls.com https://internationalpubls.com X cana-3678 178 7 5 5 NUM cana-3678 178 8 . . PUNCT cana-3678 178 9 discussion discussion NOUN cana-3678 178 10 in in ADP cana-3678 178 11 this this DET cana-3678 178 12 paper paper NOUN cana-3678 178 13 , , PUNCT cana-3678 178 14 we we PRON cana-3678 178 15 propose propose VERB cana-3678 178 16 a a DET cana-3678 178 17 method method NOUN cana-3678 178 18 to to PART cana-3678 178 19 find find VERB cana-3678 178 20 solution solution NOUN cana-3678 178 21 of of ADP cana-3678 178 22 nonlinear nonlinear ADJ cana-3678 178 23 model model NOUN cana-3678 178 24 of of ADP cana-3678 178 25 black black NOUN cana-3678 178 26 - - PUNCT cana-3678 178 27 scholes schole NOUN cana-3678 178 28 with with ADP cana-3678 178 29 transaction transaction NOUN cana-3678 178 30 costs cost NOUN cana-3678 178 31 and and CCONJ cana-3678 178 32 illiquid illiquid ADJ cana-3678 178 33 market market NOUN cana-3678 178 34 for for ADP cana-3678 178 35 european european ADJ cana-3678 178 36 call call NOUN cana-3678 178 37 option option NOUN cana-3678 178 38 with with ADP cana-3678 178 39 given give VERB cana-3678 178 40 terminal terminal ADJ cana-3678 178 41 boundary boundary ADJ cana-3678 178 42 conditions condition NOUN cana-3678 178 43 . . PUNCT cana-3678 179 1 the the DET cana-3678 179 2 proposed propose VERB cana-3678 179 3 method method NOUN cana-3678 179 4 shows show VERB cana-3678 179 5 how how SCONJ cana-3678 179 6 the the DET cana-3678 179 7 nonlinear nonlinear ADJ cana-3678 179 8 partial partial ADJ cana-3678 179 9 differential differential NOUN cana-3678 179 10 equation equation NOUN cana-3678 179 11 of of ADP cana-3678 179 12 black black ADJ cana-3678 179 13 - - PUNCT cana-3678 179 14 scholes schole NOUN cana-3678 179 15 is be AUX cana-3678 179 16 converted convert VERB cana-3678 179 17 into into ADP cana-3678 179 18 nonlinear nonlinear ADJ cana-3678 179 19 ordinary ordinary ADJ cana-3678 179 20 differential differential ADJ cana-3678 179 21 equation equation NOUN cana-3678 179 22 using use VERB cana-3678 179 23 semidiscretization semidiscretization ADJ cana-3678 179 24 technique technique NOUN cana-3678 179 25 of of ADP cana-3678 179 26 finite finite ADJ cana-3678 179 27 difference difference NOUN cana-3678 179 28 method method NOUN cana-3678 179 29 . . PUNCT cana-3678 180 1 we we PRON cana-3678 180 2 have have AUX cana-3678 180 3 used use VERB cana-3678 180 4 deep deep ADJ cana-3678 180 5 learning learning NOUN cana-3678 180 6 based base VERB cana-3678 180 7 fully fully ADV cana-3678 180 8 connected connect VERB cana-3678 180 9 neural neural ADJ cana-3678 180 10 network network NOUN cana-3678 180 11 ( ( PUNCT cana-3678 180 12 fcnn fcnn PROPN cana-3678 180 13 ) ) PUNCT cana-3678 180 14 to to PART cana-3678 180 15 solve solve VERB cana-3678 180 16 converted convert VERB cana-3678 180 17 nonlinear nonlinear ADJ cana-3678 180 18 ordinary ordinary ADJ cana-3678 180 19 differential differential ADJ cana-3678 180 20 equation equation NOUN cana-3678 180 21 model model NOUN cana-3678 180 22 of of ADP cana-3678 180 23 option option NOUN cana-3678 180 24 pricing pricing NOUN cana-3678 180 25 . . PUNCT cana-3678 181 1 the the DET cana-3678 181 2 use use NOUN cana-3678 181 3 of of ADP cana-3678 181 4 the the DET cana-3678 181 5 fcnn fcnn PROPN cana-3678 181 6 presents present VERB cana-3678 181 7 a a DET cana-3678 181 8 unique unique ADJ cana-3678 181 9 method method NOUN cana-3678 181 10 for for ADP cana-3678 181 11 pricing pricing NOUN cana-3678 181 12 option option NOUN cana-3678 181 13 . . PUNCT cana-3678 182 1 experimental experimental ADJ cana-3678 182 2 results result NOUN cana-3678 182 3 verify verify VERB cana-3678 182 4 that that SCONJ cana-3678 182 5 the the DET cana-3678 182 6 suggested suggest VERB cana-3678 182 7 method method NOUN cana-3678 182 8 can can AUX cana-3678 182 9 effectively effectively ADV cana-3678 182 10 address address VERB cana-3678 182 11 the the DET cana-3678 182 12 black black ADJ cana-3678 182 13 - - PUNCT cana-3678 182 14 scholes schole NOUN cana-3678 182 15 model model NOUN cana-3678 182 16 for for ADP cana-3678 182 17 forecasting forecast VERB cana-3678 182 18 european european ADJ cana-3678 182 19 call call NOUN cana-3678 182 20 options option NOUN cana-3678 182 21 . . PUNCT cana-3678 183 1 also also ADV cana-3678 183 2 at at ADP cana-3678 183 3 jump jump NOUN cana-3678 183 4 condition condition NOUN cana-3678 183 5 , , PUNCT cana-3678 183 6 this this DET cana-3678 183 7 method method NOUN cana-3678 183 8 provides provide VERB cana-3678 183 9 best good ADJ cana-3678 183 10 accuracy accuracy NOUN cana-3678 183 11 in in ADP cana-3678 183 12 option option NOUN cana-3678 183 13 price price NOUN cana-3678 183 14 . . PUNCT cana-3678 184 1 in in ADP cana-3678 184 2 conclusion conclusion NOUN cana-3678 184 3 , , PUNCT cana-3678 184 4 we we PRON cana-3678 184 5 can can AUX cana-3678 184 6 assert assert VERB cana-3678 184 7 that that SCONJ cana-3678 184 8 the the DET cana-3678 184 9 suggested suggest VERB cana-3678 184 10 method method NOUN cana-3678 184 11 enables enable VERB cana-3678 184 12 option option NOUN cana-3678 184 13 holder holder NOUN cana-3678 184 14 to to PART cana-3678 184 15 effectively effectively ADV cana-3678 184 16 hedge hedge VERB cana-3678 184 17 the the DET cana-3678 184 18 risk risk NOUN cana-3678 184 19 in in ADP cana-3678 184 20 financial financial ADJ cana-3678 184 21 market market NOUN cana-3678 184 22 , , PUNCT cana-3678 184 23 considering consider VERB cana-3678 184 24 nonlinear nonlinear ADJ cana-3678 184 25 factors factor NOUN cana-3678 184 26 such such ADJ cana-3678 184 27 as as ADP cana-3678 184 28 transaction transaction NOUN cana-3678 184 29 costs cost NOUN cana-3678 184 30 and and CCONJ cana-3678 184 31 illiquid illiquid ADJ cana-3678 184 32 markets market NOUN cana-3678 184 33 in in ADP cana-3678 184 34 the the DET cana-3678 184 35 case case NOUN cana-3678 184 36 of of ADP cana-3678 184 37 european european ADJ cana-3678 184 38 call call NOUN cana-3678 184 39 options option NOUN cana-3678 184 40 and and CCONJ cana-3678 184 41 will will AUX cana-3678 184 42 gain gain VERB cana-3678 184 43 significantly significantly ADV cana-3678 184 44 because because SCONJ cana-3678 184 45 the the DET cana-3678 184 46 call call NOUN cana-3678 184 47 options option NOUN cana-3678 184 48 are be AUX cana-3678 184 49 more more ADV cana-3678 184 50 probable probable ADJ cana-3678 184 51 to to PART cana-3678 184 52 finish finish VERB cana-3678 184 53 in in ADP cana-3678 184 54 the the DET cana-3678 184 55 money money NOUN cana-3678 184 56 . . PUNCT cana-3678 185 1 references reference NOUN cana-3678 185 2 [ [ X cana-3678 185 3 1 1 NUM cana-3678 185 4 ] ] X cana-3678 185 5 black black ADJ cana-3678 185 6 , , PUNCT cana-3678 185 7 f. f. PROPN cana-3678 185 8 and and CCONJ cana-3678 185 9 scholes schole NOUN cana-3678 185 10 , , PUNCT cana-3678 185 11 m. m. NOUN cana-3678 185 12 ( ( PUNCT cana-3678 185 13 1973 1973 NUM cana-3678 185 14 ) ) PUNCT cana-3678 185 15 the the DET cana-3678 185 16 pricing pricing NOUN cana-3678 185 17 of of ADP cana-3678 185 18 options option NOUN cana-3678 185 19 and and CCONJ cana-3678 185 20 corporate corporate ADJ cana-3678 185 21 liabilities liability NOUN cana-3678 185 22 . . PUNCT cana-3678 186 1 journal journal NOUN cana-3678 186 2 of of ADP cana-3678 186 3 political political ADJ cana-3678 186 4 economy economy NOUN cana-3678 186 5 , , PUNCT cana-3678 186 6 81 81 NUM cana-3678 186 7 , , PUNCT cana-3678 186 8 637 637 NUM cana-3678 186 9 - - SYM cana-3678 186 10 654 654 NUM cana-3678 186 11 . . PUNCT cana-3678 187 1 https://doi.org/10.1086/260062 https://doi.org/10.1086/260062 PRON cana-3678 188 1 [ [ X cana-3678 188 2 2 2 NUM cana-3678 188 3 ] ] X cana-3678 188 4 dokuchaev dokuchaev PROPN cana-3678 188 5 , , PUNCT cana-3678 188 6 n.g n.g PROPN cana-3678 188 7 . . PROPN cana-3678 188 8 and and CCONJ cana-3678 188 9 savkin savkin PROPN cana-3678 188 10 , , PUNCT cana-3678 188 11 a.v a.v PROPN cana-3678 188 12 . . PROPN cana-3678 188 13 ( ( PUNCT cana-3678 188 14 1998 1998 NUM cana-3678 188 15 ) ) PUNCT cana-3678 188 16 the the DET cana-3678 188 17 pricing pricing NOUN cana-3678 188 18 of of ADP cana-3678 188 19 options option NOUN cana-3678 188 20 in in ADP cana-3678 188 21 a a DET cana-3678 188 22 financial financial ADJ cana-3678 188 23 market market NOUN cana-3678 188 24 model model NOUN cana-3678 188 25 with with ADP cana-3678 188 26 transaction transaction NOUN cana-3678 188 27 costs cost NOUN cana-3678 188 28 and and CCONJ cana-3678 188 29 uncertain uncertain ADJ cana-3678 188 30 volatility volatility NOUN cana-3678 188 31 . . PUNCT cana-3678 189 1 journal journal NOUN cana-3678 189 2 of of ADP cana-3678 189 3 multinational multinational ADJ cana-3678 189 4 financial financial ADJ cana-3678 189 5 management management NOUN cana-3678 189 6 , , PUNCT cana-3678 189 7 8 8 NUM cana-3678 189 8 , , PUNCT cana-3678 189 9 353 353 NUM cana-3678 189 10 -364 -364 NOUN cana-3678 189 11 . . PUNCT cana-3678 190 1 https://doi.org/10.1016/s1042-444x(98)00036-x https://doi.org/10.1016/s1042-444x(98)00036-x PROPN cana-3678 190 2 [ [ X cana-3678 190 3 3 3 NUM cana-3678 190 4 ] ] X cana-3678 190 5 florescu florescu NOUN cana-3678 190 6 , , PUNCT cana-3678 190 7 i. i. PROPN cana-3678 190 8 , , PUNCT cana-3678 190 9 mariant mariant PROPN cana-3678 190 10 , , PUNCT cana-3678 190 11 m.c m.c PROPN cana-3678 190 12 . . PROPN cana-3678 190 13 and and CCONJ cana-3678 190 14 sengupta sengupta NOUN cana-3678 190 15 , , PUNCT cana-3678 190 16 i. i. NOUN cana-3678 190 17 ( ( PUNCT cana-3678 190 18 2014 2014 NUM cana-3678 190 19 ) ) PUNCT cana-3678 190 20 option option NOUN cana-3678 190 21 pricing pricing NOUN cana-3678 190 22 with with ADP cana-3678 190 23 transaction transaction NOUN cana-3678 190 24 costs cost NOUN cana-3678 190 25 and and CCONJ cana-3678 190 26 stochastic stochastic ADJ cana-3678 190 27 volatility volatility NOUN cana-3678 190 28 . . PUNCT cana-3678 191 1 electronic electronic ADJ cana-3678 191 2 journal journal NOUN cana-3678 191 3 of of ADP cana-3678 191 4 differential differential ADJ cana-3678 191 5 equations equation NOUN cana-3678 191 6 , , PUNCT cana-3678 191 7 2014 2014 NUM cana-3678 191 8 , , PUNCT cana-3678 191 9 1 1 NUM cana-3678 191 10 - - SYM cana-3678 191 11 19 19 NUM cana-3678 191 12 [ [ SYM cana-3678 191 13 4 4 NUM cana-3678 191 14 ] ] PUNCT cana-3678 191 15 k. k. PROPN cana-3678 191 16 ronnie ronnie PROPN cana-3678 191 17 sircar sircar PROPN cana-3678 191 18 & & CCONJ cana-3678 191 19 george george PROPN cana-3678 191 20 papanicolaou papanicolaou PROPN cana-3678 191 21 . . PUNCT cana-3678 192 1 ( ( PUNCT cana-3678 192 2 1998 1998 NUM cana-3678 192 3 ) ) PUNCT cana-3678 192 4 general general ADJ cana-3678 192 5 black black ADJ cana-3678 192 6 - - PUNCT cana-3678 192 7 scholes schole NOUN cana-3678 192 8 models model NOUN cana-3678 192 9 accounting account VERB cana-3678 192 10 for for ADP cana-3678 192 11 increased increase VERB cana-3678 192 12 market market NOUN cana-3678 192 13 volatility volatility NOUN cana-3678 192 14 from from ADP cana-3678 192 15 hedging hedge VERB cana-3678 192 16 strategies strategy NOUN cana-3678 192 17 , , PUNCT cana-3678 192 18 applied apply VERB cana-3678 192 19 mathematical mathematical ADJ cana-3678 192 20 finance finance NOUN cana-3678 192 21 , , PUNCT cana-3678 192 22 5:1 5:1 NUM cana-3678 192 23 , , PUNCT cana-3678 192 24 45 45 NUM cana-3678 192 25 -82 -82 NUM cana-3678 192 26 , , PUNCT cana-3678 192 27 doi doi NOUN cana-3678 192 28 : : PUNCT cana-3678 192 29 10.1080/135048698334727 10.1080/135048698334727 NUM cana-3678 193 1 [ [ X cana-3678 193 2 5 5 NUM cana-3678 193 3 ] ] X cana-3678 193 4 gulen gulen VERB cana-3678 193 5 , , PUNCT cana-3678 193 6 seda seda NOUN cana-3678 193 7 and and CCONJ cana-3678 193 8 popescu popescu PROPN cana-3678 193 9 , , PUNCT cana-3678 193 10 catalin catalin PROPN cana-3678 193 11 and and CCONJ cana-3678 193 12 sari sari PROPN cana-3678 193 13 , , PUNCT cana-3678 193 14 murat murat PROPN cana-3678 193 15 . . PUNCT cana-3678 194 1 ( ( PUNCT cana-3678 194 2 2019 2019 NUM cana-3678 194 3 ) ) PUNCT cana-3678 194 4 a a DET cana-3678 194 5 new new ADJ cana-3678 194 6 approach approach NOUN cana-3678 194 7 for for ADP cana-3678 194 8 the the DET cana-3678 194 9 black black ADJ cana-3678 194 10 - - PUNCT cana-3678 194 11 scholes schole NOUN cana-3678 194 12 model model NOUN cana-3678 194 13 with with ADP cana-3678 194 14 linear linear PROPN cana-3678 194 15 and and CCONJ cana-3678 194 16 nonlinear nonlinear ADJ cana-3678 194 17 volatilities volatility NOUN cana-3678 194 18 , , PUNCT cana-3678 194 19 journal journal NOUN cana-3678 194 20 of of ADP cana-3678 194 21 mathematics,7(8),760 mathematics,7(8),760 PROPN cana-3678 194 22 . . PUNCT cana-3678 195 1 [ [ X cana-3678 195 2 6 6 NUM cana-3678 195 3 ] ] X cana-3678 195 4 davis davis PROPN cana-3678 195 5 , , PUNCT cana-3678 195 6 mark mark PROPN cana-3678 195 7 ha ha INTJ cana-3678 195 8 and and CCONJ cana-3678 195 9 panas panas PROPN cana-3678 195 10 , , PUNCT cana-3678 195 11 vassilios vassilio VERB cana-3678 195 12 g g PROPN cana-3678 195 13 and and CCONJ cana-3678 195 14 zariphopoulou zariphopoulou NOUN cana-3678 195 15 , , PUNCT cana-3678 195 16 thaleia thaleia NOUN cana-3678 195 17 . . PUNCT cana-3678 196 1 ( ( PUNCT cana-3678 196 2 1993 1993 NUM cana-3678 196 3 ) ) PUNCT cana-3678 196 4 european european ADJ cana-3678 196 5 option option NOUN cana-3678 196 6 pricing pricing NOUN cana-3678 196 7 with with ADP cana-3678 196 8 transaction transaction NOUN cana-3678 196 9 costs cost NOUN cana-3678 196 10 , , PUNCT cana-3678 196 11 siam siam ADJ cana-3678 196 12 journal journal NOUN cana-3678 196 13 on on ADP cana-3678 196 14 control control NOUN cana-3678 196 15 and and CCONJ cana-3678 196 16 optimization,31(2 optimization,31(2 PROPN cana-3678 196 17 ) ) PUNCT cana-3678 196 18 , , PUNCT cana-3678 196 19 470 470 NUM cana-3678 196 20 - - SYM cana-3678 196 21 493 493 NUM cana-3678 196 22 . . PUNCT cana-3678 197 1 [ [ X cana-3678 197 2 7 7 NUM cana-3678 197 3 ] ] PUNCT cana-3678 197 4 barles barle NOUN cana-3678 197 5 , , PUNCT cana-3678 197 6 guy guy NOUN cana-3678 197 7 and and CCONJ cana-3678 197 8 soner soner NOUN cana-3678 197 9 , , PUNCT cana-3678 197 10 halil halil PROPN cana-3678 197 11 mete mete PROPN cana-3678 197 12 . . PUNCT cana-3678 198 1 ( ( PUNCT cana-3678 198 2 1998 1998 NUM cana-3678 198 3 ) ) PUNCT cana-3678 198 4 option option NOUN cana-3678 198 5 pricing pricing NOUN cana-3678 198 6 with with ADP cana-3678 198 7 transaction transaction NOUN cana-3678 198 8 costs cost NOUN cana-3678 198 9 and and CCONJ cana-3678 198 10 a a DET cana-3678 198 11 nonlinear nonlinear ADJ cana-3678 198 12 black black ADJ cana-3678 198 13 -scholes -schole NOUN cana-3678 198 14 equation equation NOUN cana-3678 198 15 , , PUNCT cana-3678 198 16 finance finance NOUN cana-3678 198 17 and and CCONJ cana-3678 198 18 stochastics,2 stochastics,2 NOUN cana-3678 198 19 , , PUNCT cana-3678 198 20 369 369 NUM cana-3678 198 21 - - SYM cana-3678 198 22 397 397 NUM cana-3678 198 23 . . PUNCT cana-3678 199 1 [ [ X cana-3678 199 2 8 8 NUM cana-3678 199 3 ] ] X cana-3678 199 4 liu liu PROPN cana-3678 199 5 , , PUNCT cana-3678 199 6 h. h. PROPN cana-3678 199 7 and and CCONJ cana-3678 199 8 yong yong PROPN cana-3678 199 9 , , PUNCT cana-3678 199 10 j. j. PROPN cana-3678 199 11 ( ( PUNCT cana-3678 199 12 2005 2005 NUM cana-3678 199 13 ) ) PUNCT cana-3678 199 14 option option NOUN cana-3678 199 15 pricing pricing NOUN cana-3678 199 16 with with ADP cana-3678 199 17 an an DET cana-3678 199 18 illiquid illiquid ADJ cana-3678 199 19 asset asset NOUN cana-3678 199 20 market market NOUN cana-3678 199 21 . . PUNCT cana-3678 200 1 journal journal NOUN cana-3678 200 2 of of ADP cana-3678 200 3 economic economic ADJ cana-3678 200 4 dynamics dynamic NOUN cana-3678 200 5 & & CCONJ cana-3678 200 6 control control PROPN cana-3678 200 7 , , PUNCT cana-3678 200 8 29 29 NUM cana-3678 200 9 , , PUNCT cana-3678 200 10 2125 2125 NUM cana-3678 200 11 - - SYM cana-3678 200 12 2156 2156 NUM cana-3678 200 13 . . PUNCT cana-3678 201 1 https://doi.org/10.1016/j.jedc.2004.11.004 https://doi.org/10.1016/j.jedc.2004.11.004 NOUN cana-3678 201 2 [ [ X cana-3678 201 3 9 9 NUM cana-3678 201 4 ] ] X cana-3678 201 5 glover glover PROPN cana-3678 201 6 , , PUNCT cana-3678 201 7 k.j k.j PROPN cana-3678 201 8 . . PROPN cana-3678 201 9 , , PUNCT cana-3678 201 10 duck duck NOUN cana-3678 201 11 , , PUNCT cana-3678 201 12 p.w p.w PROPN cana-3678 201 13 . . PROPN cana-3678 201 14 and and CCONJ cana-3678 201 15 newton newton PROPN cana-3678 201 16 , , PUNCT cana-3678 201 17 d.p d.p PROPN cana-3678 201 18 . . PROPN cana-3678 202 1 ( ( PUNCT cana-3678 202 2 2010 2010 NUM cana-3678 202 3 ) ) PUNCT cana-3678 202 4 on on ADP cana-3678 202 5 nonlinear nonlinear ADJ cana-3678 202 6 models model NOUN cana-3678 202 7 of of ADP cana-3678 202 8 markets market NOUN cana-3678 202 9 with with ADP cana-3678 202 10 finite finite ADJ cana-3678 202 11 liquidity liquidity NOUN cana-3678 202 12 : : PUNCT cana-3678 202 13 some some DET cana-3678 202 14 cautionary cautionary ADJ cana-3678 202 15 notes note NOUN cana-3678 202 16 . . PUNCT cana-3678 203 1 siam siam PROPN cana-3678 203 2 journal journal PROPN cana-3678 203 3 on on ADP cana-3678 203 4 applied apply VERB cana-3678 203 5 mathematics mathematic NOUN cana-3678 203 6 , , PUNCT cana-3678 203 7 70 70 NUM cana-3678 203 8 , , PUNCT cana-3678 203 9 3252 3252 NUM cana-3678 203 10 - - SYM cana-3678 203 11 3271 3271 NUM cana-3678 203 12 . . PUNCT cana-3678 203 13 https://doi.org/10.1137/080736119 https://doi.org/10.1137/080736119 X cana-3678 204 1 [ [ X cana-3678 204 2 10 10 NUM cana-3678 204 3 ] ] SYM cana-3678 204 4 pirvu pirvu NOUN cana-3678 204 5 , , PUNCT cana-3678 204 6 t.a t.a PROPN cana-3678 204 7 . . PROPN cana-3678 204 8 and and CCONJ cana-3678 204 9 yazdanian yazdanian NOUN cana-3678 204 10 , , PUNCT cana-3678 204 11 a. a. PROPN cana-3678 204 12 ( ( PUNCT cana-3678 204 13 2015 2015 NUM cana-3678 204 14 ) ) PUNCT cana-3678 204 15 numerical numerical ADJ cana-3678 204 16 analysis analysis NOUN cana-3678 204 17 for for ADP cana-3678 204 18 spread spread ADJ cana-3678 204 19 option option NOUN cana-3678 204 20 pricing pricing NOUN cana-3678 204 21 model model NOUN cana-3678 204 22 in in ADP cana-3678 204 23 illiquid illiquid ADJ cana-3678 204 24 underlying underlying ADJ cana-3678 204 25 asset asset NOUN cana-3678 204 26 market market NOUN cana-3678 204 27 : : PUNCT cana-3678 204 28 full full ADJ cana-3678 204 29 feedback feedback NOUN cana-3678 204 30 model model NOUN cana-3678 204 31 . . PUNCT cana-3678 205 1 applied apply VERB cana-3678 205 2 mathematics mathematics PROPN cana-3678 205 3 & & CCONJ cana-3678 205 4 information information NOUN cana-3678 205 5 sciences sciences PROPN cana-3678 205 6 , , PUNCT cana-3678 205 7 1271 1271 NUM cana-3678 205 8 -1281 -1281 PRON cana-3678 205 9 . . PUNCT cana-3678 206 1 https://doi.org/10.18576/amis/100406 https://doi.org/10.18576/amis/100406 NOUN cana-3678 207 1 [ [ X cana-3678 207 2 11 11 NUM cana-3678 207 3 ] ] X cana-3678 207 4 el el PROPN cana-3678 207 5 - - PROPN cana-3678 207 6 khatib khatib PROPN cana-3678 207 7 , , PUNCT cana-3678 207 8 y. y. PROPN cana-3678 207 9 and and CCONJ cana-3678 207 10 hatemi hatemi PROPN cana-3678 207 11 - - PUNCT cana-3678 207 12 j j PROPN cana-3678 207 13 , , PUNCT cana-3678 207 14 a. a. PROPN cana-3678 207 15 ( ( PUNCT cana-3678 207 16 2013 2013 NUM cana-3678 207 17 ) ) PUNCT cana-3678 207 18 on on ADP cana-3678 207 19 option option NOUN cana-3678 207 20 pricing pricing NOUN cana-3678 207 21 in in ADP cana-3678 207 22 illiquid illiquid ADJ cana-3678 207 23 markets market NOUN cana-3678 207 24 with with ADP cana-3678 207 25 jumps jump NOUN cana-3678 207 26 . . PUNCT cana-3678 208 1 international international ADJ cana-3678 208 2 scholarly scholarly ADJ cana-3678 208 3 research research NOUN cana-3678 208 4 notices notice NOUN cana-3678 208 5 , , PUNCT cana-3678 208 6 2013 2013 NUM cana-3678 208 7 , , PUNCT cana-3678 208 8 article article NOUN cana-3678 208 9 i i PROPN cana-3678 208 10 d d PROPN cana-3678 208 11 567071 567071 NUM cana-3678 208 12 . . PUNCT cana-3678 209 1 https://doi.org/10.1155/2013/567071 https://doi.org/10.1155/2013/567071 PROPN cana-3678 210 1 [ [ X cana-3678 210 2 12 12 NUM cana-3678 210 3 ] ] X cana-3678 210 4 agana agana PROPN cana-3678 210 5 , , PUNCT cana-3678 210 6 f. f. PROPN cana-3678 210 7 , , PUNCT cana-3678 210 8 makinde makinde PROPN cana-3678 210 9 , , PUNCT cana-3678 210 10 o.d o.d PROPN cana-3678 210 11 . . PROPN cana-3678 210 12 and and CCONJ cana-3678 210 13 theuri theuri PROPN cana-3678 210 14 , , PUNCT cana-3678 210 15 d.m d.m PROPN cana-3678 210 16 . . PUNCT cana-3678 211 1 ( ( PUNCT cana-3678 211 2 2016 2016 NUM cana-3678 211 3 ) ) PUNCT cana-3678 211 4 numerical numerical ADJ cana-3678 211 5 treatment treatment NOUN cana-3678 211 6 of of ADP cana-3678 211 7 a a DET cana-3678 211 8 generalized generalized ADJ cana-3678 211 9 black black ADJ cana-3678 211 10 -scholes -schole NOUN cana-3678 211 11 model model NOUN cana-3678 211 12 for for ADP cana-3678 211 13 options option NOUN cana-3678 211 14 pricing pricing NOUN cana-3678 211 15 in in ADP cana-3678 211 16 an an DET cana-3678 211 17 illiquid illiquid ADJ cana-3678 211 18 financial financial ADJ cana-3678 211 19 market market NOUN cana-3678 211 20 with with ADP cana-3678 211 21 transections transection NOUN cana-3678 211 22 costs cost NOUN cana-3678 211 23 . . PUNCT cana-3678 212 1 global global ADJ cana-3678 212 2 journal journal NOUN cana-3678 212 3 of of ADP cana-3678 212 4 pure pure ADJ cana-3678 212 5 and and CCONJ cana-3678 212 6 applied applied ADJ cana-3678 212 7 mathematics mathematic NOUN cana-3678 212 8 , , PUNCT cana-3678 212 9 12 12 NUM cana-3678 212 10 , , PUNCT cana-3678 212 11 4349 4349 NUM cana-3678 212 12 - - SYM cana-3678 212 13 4361 4361 NUM cana-3678 212 14 . . PUNCT cana-3678 213 1 [ [ X cana-3678 213 2 13 13 NUM cana-3678 213 3 ] ] PUNCT cana-3678 213 4 praewnapa praewnapa NOUN cana-3678 213 5 seelama seelama PROPN cana-3678 213 6 , , PUNCT cana-3678 213 7 dawud dawud PROPN cana-3678 213 8 thongtha thongtha PROPN cana-3678 213 9 . . PUNCT cana-3678 214 1 ( ( PUNCT cana-3678 214 2 2021 2021 NUM cana-3678 214 3 ) ) PUNCT cana-3678 214 4 option option NOUN cana-3678 214 5 pricing pricing NOUN cana-3678 214 6 model model NOUN cana-3678 214 7 with with ADP cana-3678 214 8 transaction transaction NOUN cana-3678 214 9 costs cost NOUN cana-3678 214 10 and and CCONJ cana-3678 214 11 jumps jump VERB cana-3678 214 12 in in ADP cana-3678 214 13 illiquid illiquid ADJ cana-3678 214 14 markets market NOUN cana-3678 214 15 . . PUNCT cana-3678 215 1 journal journal PROPN cana-3678 215 2 of of ADP cana-3678 215 3 mathematical mathematical ADJ cana-3678 215 4 finance finance NOUN cana-3678 215 5 , , PUNCT cana-3678 215 6 11 11 NUM cana-3678 215 7 , , PUNCT cana-3678 215 8 361 361 NUM cana-3678 215 9 - - SYM cana-3678 215 10 372 372 NUM cana-3678 215 11 . . PUNCT cana-3678 216 1 [ [ X cana-3678 216 2 14 14 NUM cana-3678 216 3 ] ] X cana-3678 216 4 strang strang PROPN cana-3678 216 5 , , PUNCT cana-3678 216 6 g. g. PROPN cana-3678 216 7 , , PUNCT cana-3678 216 8 fix fix NOUN cana-3678 216 9 , , PUNCT cana-3678 216 10 g. g. PROPN cana-3678 216 11 j. j. PROPN cana-3678 216 12 , , PUNCT cana-3678 216 13 1973 1973 NUM cana-3678 216 14 . . PUNCT cana-3678 217 1 an an DET cana-3678 217 2 analysis analysis NOUN cana-3678 217 3 of of ADP cana-3678 217 4 the the DET cana-3678 217 5 finite finite ADJ cana-3678 217 6 element element NOUN cana-3678 217 7 method method NOUN cana-3678 217 8 . . PUNCT cana-3678 218 1 prentice prentice NOUN cana-3678 218 2 - - PUNCT cana-3678 218 3 hall hall PROPN cana-3678 218 4 , , PUNCT cana-3678 218 5 inc inc PROPN cana-3678 218 6 . . PROPN cana-3678 218 7 , , PUNCT cana-3678 218 8 englewood englewood PROPN cana-3678 218 9 cliffs cliffs PROPN cana-3678 218 10 , , PUNCT cana-3678 218 11 n. n. PROPN cana-3678 218 12 j. j. PROPN cana-3678 218 13 , , PUNCT cana-3678 218 14 prentice prentice NOUN cana-3678 218 15 - - PUNCT cana-3678 218 16 hall hall NOUN cana-3678 218 17 series series NOUN cana-3678 218 18 in in ADP cana-3678 218 19 automatic automatic ADJ cana-3678 218 20 computation computation NOUN cana-3678 218 21 . . PUNCT cana-3678 219 1 [ [ X cana-3678 219 2 15 15 NUM cana-3678 219 3 ] ] PUNCT cana-3678 219 4 bochev bochev PROPN cana-3678 219 5 , , PUNCT cana-3678 219 6 p. p. PROPN cana-3678 219 7 b. b. PROPN cana-3678 219 8 , , PUNCT cana-3678 219 9 gunzburger gunzburger NOUN cana-3678 219 10 , , PUNCT cana-3678 219 11 m. m. NOUN cana-3678 219 12 d. d. PROPN cana-3678 219 13 ( ( PUNCT cana-3678 219 14 2009 2009 NUM cana-3678 219 15 ) ) PUNCT cana-3678 219 16 least least ADJ cana-3678 219 17 - - PUNCT cana-3678 219 18 squares square NOUN cana-3678 219 19 finite finite PROPN cana-3678 219 20 element element NOUN cana-3678 219 21 methods method NOUN cana-3678 219 22 . . PUNCT cana-3678 220 1 vol vol NOUN cana-3678 220 2 . . PROPN cana-3678 220 3 166 166 NUM cana-3678 220 4 of of ADP cana-3678 220 5 applied apply VERB cana-3678 220 6 mathematical mathematical ADJ cana-3678 220 7 sciences science NOUN cana-3678 220 8 . . PUNCT cana-3678 221 1 springer springer NOUN cana-3678 221 2 , , PUNCT cana-3678 221 3 new new PROPN cana-3678 221 4 york york PROPN cana-3678 221 5 . . PUNCT cana-3678 222 1 https://doi-org.ezproxy.lib.utexas.edu/10.1007 https://doi-org.ezproxy.lib.utexas.edu/10.1007 ADJ cana-3678 222 2 https://doi.org/10.1086/260062 https://doi.org/10.1086/260062 PRON cana-3678 222 3 https://doi.org/10.1016/j.jedc.2004.11.004 https://doi.org/10.1016/j.jedc.2004.11.004 VERB cana-3678 222 4 https://doi.org/10.1137/080736119 https://doi.org/10.1137/080736119 PROPN cana-3678 222 5 https://doi.org/10.18576/amis/100406 https://doi.org/10.18576/amis/100406 PROPN cana-3678 222 6 https://doi.org/10.1155/2013/567071 https://doi.org/10.1155/2013/567071 ADJ cana-3678 222 7 https://doi-org.ezproxy.lib.utexas.edu/10.1007 https://doi-org.ezproxy.lib.utexas.edu/10.1007 ADJ cana-3678 222 8 communications communication NOUN cana-3678 222 9 on on ADP cana-3678 222 10 applied apply VERB cana-3678 222 11 nonlinear nonlinear ADJ cana-3678 222 12 analysis analysis NOUN cana-3678 222 13 issn issn NOUN cana-3678 222 14 : : PUNCT cana-3678 222 15 1074 1074 NUM cana-3678 222 16 - - PUNCT cana-3678 222 17 133x 133x NUM cana-3678 222 18 vol vol NOUN cana-3678 222 19 32 32 NUM cana-3678 222 20 no no NOUN cana-3678 222 21 . . PUNCT cana-3678 223 1 8s 8s PROPN cana-3678 223 2 ( ( PUNCT cana-3678 223 3 2025 2025 NUM cana-3678 223 4 ) ) PUNCT cana-3678 223 5 328 328 NUM cana-3678 223 6 https://internationalpubls.com https://internationalpubls.com X cana-3678 224 1 [ [ X cana-3678 224 2 16 16 NUM cana-3678 224 3 ] ] X cana-3678 224 4 li li PROPN cana-3678 224 5 , , PUNCT cana-3678 224 6 x. x. PROPN cana-3678 224 7 ( ( PUNCT cana-3678 224 8 2016 2016 NUM cana-3678 224 9 ) ) PUNCT cana-3678 224 10 error error NOUN cana-3678 224 11 estimates estimate NOUN cana-3678 224 12 for for ADP cana-3678 224 13 the the DET cana-3678 224 14 moving move VERB cana-3678 224 15 least least ADJ cana-3678 224 16 - - PUNCT cana-3678 224 17 square square NOUN cana-3678 224 18 approximation approximation NOUN cana-3678 224 19 and and CCONJ cana-3678 224 20 the the DET cana-3678 224 21 element element NOUN cana-3678 224 22 - - PUNCT cana-3678 224 23 free free ADJ cana-3678 224 24 galerkin galerkin ADJ cana-3678 224 25 method method NOUN cana-3678 224 26 in in ADP cana-3678 224 27 ndimensional ndimensional ADJ cana-3678 224 28 spaces space NOUN cana-3678 224 29 . . PUNCT cana-3678 225 1 applied apply VERB cana-3678 225 2 numerical numerical ADJ cana-3678 225 3 mathematics mathematic NOUN cana-3678 225 4 . . PUNCT cana-3678 226 1 an an DET cana-3678 226 2 imacs imacs PROPN cana-3678 226 3 journal journal NOUN cana-3678 226 4 99 99 NUM cana-3678 226 5 , , PUNCT cana-3678 226 6 77–97 77–97 NUM cana-3678 226 7 . . PUNCT cana-3678 227 1 https://doiorg.ezproxy.lib.utexas.edu/10.1016 https://doiorg.ezproxy.lib.utexas.edu/10.1016 PROPN cana-3678 228 1 [ [ X cana-3678 228 2 17 17 NUM cana-3678 228 3 ] ] X cana-3678 228 4 babuΛ‡ska babuΛ‡ska PROPN cana-3678 228 5 , , PUNCT cana-3678 228 6 i. i. PROPN cana-3678 228 7 , , PUNCT cana-3678 228 8 banerjee banerjee PROPN cana-3678 228 9 , , PUNCT cana-3678 228 10 u. u. PROPN cana-3678 228 11 , , PUNCT cana-3678 228 12 osborn osborn PROPN cana-3678 228 13 , , PUNCT cana-3678 228 14 j. j. PROPN cana-3678 228 15 e. e. PROPN cana-3678 228 16 ( ( PUNCT cana-3678 228 17 2003 2003 NUM cana-3678 228 18 ) ) PUNCT cana-3678 228 19 survey survey NOUN cana-3678 228 20 of of ADP cana-3678 228 21 meshless meshless ADJ cana-3678 228 22 and and CCONJ cana-3678 228 23 generalized generalized ADJ cana-3678 228 24 finite finite ADJ cana-3678 228 25 element element NOUN cana-3678 228 26 methods method NOUN cana-3678 228 27 : : PUNCT cana-3678 228 28 a a DET cana-3678 228 29 unified unified ADJ cana-3678 228 30 approach approach NOUN cana-3678 228 31 . . PUNCT cana-3678 229 1 acta acta PROPN cana-3678 229 2 numerica numerica PROPN cana-3678 229 3 12 12 NUM cana-3678 229 4 , , PUNCT cana-3678 229 5 1–125 1–125 NUM cana-3678 229 6 . . PUNCT cana-3678 230 1 https://doi-org.ezproxy.lib.utexas.edu/10.1017/s0962492902000090 https://doi-org.ezproxy.lib.utexas.edu/10.1017/s0962492902000090 PROPN cana-3678 230 2 [ [ X cana-3678 230 3 18 18 NUM cana-3678 230 4 ] ] X cana-3678 230 5 lagaris lagaris PROPN cana-3678 230 6 , , PUNCT cana-3678 230 7 i. i. PROPN cana-3678 230 8 e. e. PROPN cana-3678 230 9 , , PUNCT cana-3678 230 10 likas likas PROPN cana-3678 230 11 , , PUNCT cana-3678 230 12 a. a. NOUN cana-3678 230 13 , , PUNCT cana-3678 230 14 fotiadis fotiadis PROPN cana-3678 230 15 , , PUNCT cana-3678 230 16 d. d. PROPN cana-3678 230 17 i. i. PROPN cana-3678 230 18 ( ( PUNCT cana-3678 230 19 1998 1998 NUM cana-3678 230 20 ) ) PUNCT cana-3678 230 21 artificial artificial ADJ cana-3678 230 22 neural neural ADJ cana-3678 230 23 networks network NOUN cana-3678 230 24 for for ADP cana-3678 230 25 solving solve VERB cana-3678 230 26 ordinary ordinary ADJ cana-3678 230 27 and and CCONJ cana-3678 230 28 partial partial ADJ cana-3678 230 29 differential differential ADJ cana-3678 230 30 equations equation NOUN cana-3678 230 31 . . PUNCT cana-3678 231 1 ieee ieee NOUN cana-3678 231 2 transactions transaction NOUN cana-3678 231 3 on on ADP cana-3678 231 4 neural neural ADJ cana-3678 231 5 networks network NOUN cana-3678 231 6 9 9 NUM cana-3678 231 7 ( ( PUNCT cana-3678 231 8 5 5 NUM cana-3678 231 9 ) ) PUNCT cana-3678 231 10 , , PUNCT cana-3678 231 11 987–1000 987–1000 NUM cana-3678 231 12 . . PUNCT cana-3678 232 1 [ [ X cana-3678 232 2 19 19 NUM cana-3678 232 3 ] ] SYM cana-3678 232 4 han han PROPN cana-3678 232 5 , , PUNCT cana-3678 232 6 j. j. PROPN cana-3678 232 7 , , PUNCT cana-3678 232 8 jentzen jentzen PROPN cana-3678 232 9 , , PUNCT cana-3678 232 10 a. a. NOUN cana-3678 232 11 , , PUNCT cana-3678 232 12 e e PROPN cana-3678 232 13 , , PUNCT cana-3678 232 14 w. w. PROPN cana-3678 232 15 ( ( PUNCT cana-3678 232 16 2018 2018 NUM cana-3678 232 17 ) ) PUNCT cana-3678 232 18 solving solve VERB cana-3678 232 19 high high ADJ cana-3678 232 20 - - PUNCT cana-3678 232 21 dimensional dimensional ADJ cana-3678 232 22 partial partial ADJ cana-3678 232 23 differential differential NOUN cana-3678 232 24 equations equation NOUN cana-3678 232 25 using use VERB cana-3678 232 26 deep deep ADJ cana-3678 232 27 learning learning NOUN cana-3678 232 28 . . PUNCT cana-3678 233 1 proceedings proceeding NOUN cana-3678 233 2 of of ADP cana-3678 233 3 the the DET cana-3678 233 4 national national PROPN cana-3678 233 5 academy academy PROPN cana-3678 233 6 of of ADP cana-3678 233 7 sciences sciences PROPN cana-3678 233 8 115 115 NUM cana-3678 233 9 ( ( PUNCT cana-3678 233 10 34 34 NUM cana-3678 233 11 ) ) PUNCT cana-3678 233 12 , , PUNCT cana-3678 233 13 8505–8510 8505–8510 NUM cana-3678 233 14 . . PUNCT cana-3678 233 15 https://www.pnas.org/content/115/34/8505 https://www.pnas.org/content/115/34/8505 PROPN cana-3678 234 1 [ [ X cana-3678 234 2 20 20 NUM cana-3678 234 3 ] ] X cana-3678 234 4 berg berg PROPN cana-3678 234 5 , , PUNCT cana-3678 234 6 j. j. PROPN cana-3678 234 7 , , PUNCT cana-3678 234 8 nystra˝um nystra˝um PROPN cana-3678 234 9 , , PUNCT cana-3678 234 10 k. k. PROPN cana-3678 234 11 ( ( PUNCT cana-3678 234 12 2019 2019 NUM cana-3678 234 13 ) ) PUNCT cana-3678 234 14 data datum NOUN cana-3678 234 15 -driven -driven ADJ cana-3678 234 16 discovery discovery NOUN cana-3678 234 17 of of ADP cana-3678 234 18 pdes pde NOUN cana-3678 234 19 in in ADP cana-3678 234 20 complex complex ADJ cana-3678 234 21 datasets dataset NOUN cana-3678 234 22 . . PUNCT cana-3678 235 1 journal journal PROPN cana-3678 235 2 of of ADP cana-3678 235 3 computational computational ADJ cana-3678 235 4 physics physics NOUN cana-3678 235 5 384 384 NUM cana-3678 235 6 , , PUNCT cana-3678 235 7 239 239 NUM cana-3678 235 8 – – PUNCT cana-3678 235 9 252 252 NUM cana-3678 235 10 . . PUNCT cana-3678 236 1 http://www.sciencedirect.com/science/article/pii/s0021999119300944 http://www.sciencedirect.com/science/article/pii/s0021999119300944 X cana-3678 237 1 [ [ X cana-3678 237 2 21 21 NUM cana-3678 237 3 ] ] X cana-3678 237 4 nabian nabian NOUN cana-3678 237 5 , , PUNCT cana-3678 237 6 m. m. NOUN cana-3678 237 7 a. a. PROPN cana-3678 237 8 , , PUNCT cana-3678 237 9 meidani meidani PROPN cana-3678 237 10 , , PUNCT cana-3678 237 11 h. h. PROPN cana-3678 237 12 ( ( PUNCT cana-3678 237 13 2019 2019 NUM cana-3678 237 14 ) ) PUNCT cana-3678 237 15 physics physics NOUN cana-3678 237 16 - - PUNCT cana-3678 237 17 driven drive VERB cana-3678 237 18 regularization regularization NOUN cana-3678 237 19 of of ADP cana-3678 237 20 deep deep ADJ cana-3678 237 21 neural neural ADJ cana-3678 237 22 networks network NOUN cana-3678 237 23 for for ADP cana-3678 237 24 enhanced enhanced ADJ cana-3678 237 25 engineering engineering NOUN cana-3678 237 26 design design NOUN cana-3678 237 27 and and CCONJ cana-3678 237 28 analysis analysis NOUN cana-3678 237 29 . . PUNCT cana-3678 237 30 journal journal NOUN cana-3678 237 31 of of ADP cana-3678 237 32 computing computing NOUN cana-3678 237 33 and and CCONJ cana-3678 237 34 information information NOUN cana-3678 237 35 science science NOUN cana-3678 237 36 in in ADP cana-3678 237 37 engineering engineering NOUN cana-3678 237 38 20 20 NUM cana-3678 237 39 ( ( PUNCT cana-3678 237 40 1 1 NUM cana-3678 237 41 ) ) PUNCT cana-3678 237 42 , , PUNCT cana-3678 237 43 011006 011006 NUM cana-3678 237 44 . . PUNCT cana-3678 238 1 url url PROPN cana-3678 238 2 https://doi.org/10.1115/1.4044507 https://doi.org/10.1115/1.4044507 PROPN cana-3678 239 1 [ [ X cana-3678 239 2 22 22 NUM cana-3678 239 3 ] ] X cana-3678 239 4 raissi raissi ADJ cana-3678 239 5 , , PUNCT cana-3678 239 6 m. m. NOUN cana-3678 239 7 , , PUNCT cana-3678 239 8 perdikaris perdikaris NOUN cana-3678 239 9 , , PUNCT cana-3678 239 10 p. p. PROPN cana-3678 239 11 , , PUNCT cana-3678 239 12 karniadakis karniadakis PROPN cana-3678 239 13 , , PUNCT cana-3678 239 14 g. g. PROPN cana-3678 239 15 ( ( PUNCT cana-3678 239 16 2019 2019 NUM cana-3678 239 17 ) ) PUNCT cana-3678 239 18 physics physics NOUN cana-3678 239 19 - - PUNCT cana-3678 239 20 informed inform VERB cana-3678 239 21 neural neural ADJ cana-3678 239 22 networks network NOUN cana-3678 239 23 : : PUNCT cana-3678 239 24 a a DET cana-3678 239 25 deep deep ADJ cana-3678 239 26 learning learning NOUN cana-3678 239 27 framework framework NOUN cana-3678 239 28 for for ADP cana-3678 239 29 solving solve VERB cana-3678 239 30 forward forward ADV cana-3678 239 31 and and CCONJ cana-3678 239 32 inverse inverse NOUN cana-3678 239 33 problems problem NOUN cana-3678 239 34 involving involve VERB cana-3678 239 35 nonlinear nonlinear ADJ cana-3678 239 36 partial partial ADJ cana-3678 239 37 differential differential NOUN cana-3678 239 38 equations equation NOUN cana-3678 239 39 . . PUNCT cana-3678 240 1 journal journal NOUN cana-3678 240 2 of of ADP cana-3678 240 3 computational computational ADJ cana-3678 240 4 physics physic NOUN cana-3678 240 5 378 378 NUM cana-3678 240 6 , , PUNCT cana-3678 240 7 686 686 NUM cana-3678 240 8 – – PUNCT cana-3678 240 9 707 707 NUM cana-3678 240 10 . . PUNCT cana-3678 241 1 http://www.sciencedirect.com/science/article/pii http://www.sciencedirect.com/science/article/pii NOUN cana-3678 241 2 [ [ X cana-3678 241 3 23 23 NUM cana-3678 241 4 ] ] PUNCT cana-3678 241 5 sirignano sirignano PROPN cana-3678 241 6 , , PUNCT cana-3678 241 7 j. j. PROPN cana-3678 241 8 , , PUNCT cana-3678 241 9 spiliopoulos spiliopoulos PROPN cana-3678 241 10 , , PUNCT cana-3678 241 11 k.(2018 k.(2018 PROPN cana-3678 241 12 ) ) PUNCT cana-3678 241 13 dgm dgm PROPN cana-3678 241 14 : : PUNCT cana-3678 241 15 a a DET cana-3678 241 16 deep deep ADJ cana-3678 241 17 learning learning NOUN cana-3678 241 18 algorithm algorithm NOUN cana-3678 241 19 for for ADP cana-3678 241 20 solving solve VERB cana-3678 241 21 partial partial ADJ cana-3678 241 22 differential differential ADJ cana-3678 241 23 equations equation NOUN cana-3678 241 24 . . PUNCT cana-3678 242 1 journal journal NOUN cana-3678 242 2 of of ADP cana-3678 242 3 computational computational ADJ cana-3678 242 4 physics physic NOUN cana-3678 242 5 375 375 NUM cana-3678 242 6 , , PUNCT cana-3678 242 7 1339 1339 NUM cana-3678 242 8 – – PUNCT cana-3678 242 9 1364 1364 NUM cana-3678 242 10 . . PUNCT cana-3678 243 1 http://www.sciencedirect.com/science/article/pii/s0021999118305527 http://www.sciencedirect.com/science/article/pii/s0021999118305527 PUNCT cana-3678 244 1 [ [ X cana-3678 244 2 24 24 NUM cana-3678 244 3 ] ] PUNCT cana-3678 244 4 agana agana PROPN cana-3678 244 5 , , PUNCT cana-3678 244 6 f. f. PROPN cana-3678 244 7 , , PUNCT cana-3678 244 8 makinde makinde PROPN cana-3678 244 9 , , PUNCT cana-3678 244 10 o.d o.d PROPN cana-3678 244 11 . . PROPN cana-3678 244 12 and and CCONJ cana-3678 244 13 theuri theuri PROPN cana-3678 244 14 , , PUNCT cana-3678 244 15 d.m d.m PROPN cana-3678 244 16 . . PUNCT cana-3678 245 1 ( ( PUNCT cana-3678 245 2 2016 2016 NUM cana-3678 245 3 ) ) PUNCT cana-3678 245 4 numerical numerical ADJ cana-3678 245 5 treatment treatment NOUN cana-3678 245 6 of of ADP cana-3678 245 7 a a DET cana-3678 245 8 generalized generalized ADJ cana-3678 245 9 black black ADJ cana-3678 245 10 -scholes -schole NOUN cana-3678 245 11 model model NOUN cana-3678 245 12 for for ADP cana-3678 245 13 options option NOUN cana-3678 245 14 pricing pricing NOUN cana-3678 245 15 in in ADP cana-3678 245 16 an an DET cana-3678 245 17 illiquid illiquid ADJ cana-3678 245 18 financial financial ADJ cana-3678 245 19 market market NOUN cana-3678 245 20 with with ADP cana-3678 245 21 transections transection NOUN cana-3678 245 22 costs cost NOUN cana-3678 245 23 . . PUNCT cana-3678 246 1 global global ADJ cana-3678 246 2 journal journal NOUN cana-3678 246 3 of of ADP cana-3678 246 4 pure pure ADJ cana-3678 246 5 and and CCONJ cana-3678 246 6 applied applied ADJ cana-3678 246 7 mathematics mathematic NOUN cana-3678 246 8 , , PUNCT cana-3678 246 9 12 12 NUM cana-3678 246 10 , , PUNCT cana-3678 246 11 4349 4349 NUM cana-3678 246 12 - - SYM cana-3678 246 13 4361 4361 NUM cana-3678 246 14 . . PUNCT cana-3678 247 1 [ [ X cana-3678 247 2 25 25 NUM cana-3678 247 3 ] ] X cana-3678 247 4 r. r. X cana-3678 247 5 lburden lburden PROPN cana-3678 247 6 and and CCONJ cana-3678 247 7 j.d j.d PROPN cana-3678 247 8 . . PROPN cana-3678 247 9 faires faire NOUN cana-3678 247 10 . . PUNCT cana-3678 248 1 ( ( PUNCT cana-3678 248 2 2010 2010 NUM cana-3678 248 3 ) ) PUNCT cana-3678 248 4 numerical numerical ADJ cana-3678 248 5 analysis analysis NOUN cana-3678 248 6 . . PUNCT cana-3678 249 1 cengage cengage PROPN cana-3678 249 2 learning learning PROPN cana-3678 249 3 . . PUNCT cana-3678 250 1 [ [ X cana-3678 250 2 26 26 NUM cana-3678 250 3 ] ] PUNCT cana-3678 250 4 barles barle NOUN cana-3678 250 5 , , PUNCT cana-3678 250 6 guy guy NOUN cana-3678 250 7 , , PUNCT cana-3678 250 8 and and CCONJ cana-3678 250 9 halil halil PROPN cana-3678 250 10 mete mete PROPN cana-3678 250 11 soner soner NOUN cana-3678 250 12 . . PUNCT cana-3678 251 1 " " PUNCT cana-3678 251 2 option option NOUN cana-3678 251 3 pricing pricing NOUN cana-3678 251 4 with with ADP cana-3678 251 5 transaction transaction NOUN cana-3678 251 6 costs cost NOUN cana-3678 251 7 and and CCONJ cana-3678 251 8 a a DET cana-3678 251 9 nonlinear nonlinear ADJ cana-3678 251 10 black black ADJ cana-3678 251 11 -scholes -schole NOUN cana-3678 251 12 equation equation NOUN cana-3678 251 13 . . PUNCT cana-3678 251 14 " " PUNCT cana-3678 252 1 finance finance NOUN cana-3678 252 2 and and CCONJ cana-3678 252 3 stochastics stochastic NOUN cana-3678 252 4 2 2 NUM cana-3678 252 5 ( ( PUNCT cana-3678 252 6 1998 1998 NUM cana-3678 252 7 ): ): PUNCT cana-3678 252 8 369 369 NUM cana-3678 252 9 - - SYM cana-3678 252 10 397 397 NUM cana-3678 252 11 . . PUNCT cana-3678 253 1 https://doi-org.ezproxy.lib.utexas.edu/10.1016 https://doi-org.ezproxy.lib.utexas.edu/10.1016 PROPN cana-3678 253 2 https://doi-org.ezproxy.lib.utexas.edu/10.1016 https://doi-org.ezproxy.lib.utexas.edu/10.1016 VERB cana-3678 253 3 https://doi-org.ezproxy.lib.utexas.edu/10.1017/s0962492902000090 https://doi-org.ezproxy.lib.utexas.edu/10.1017/s0962492902000090 PROPN cana-3678 253 4 https://www.pnas.org/content/115/34/8505 https://www.pnas.org/content/115/34/8505 PROPN cana-3678 253 5 http://www.sciencedirect.com/science/article/pii/s0021999119300944 http://www.sciencedirect.com/science/article/pii/s0021999119300944 X cana-3678 253 6 https://doi.org/10.1115/1.4044507 https://doi.org/10.1115/1.4044507 PROPN cana-3678 253 7 http://www.sciencedirect.com/science/article/pii http://www.sciencedirect.com/science/article/pii PROPN cana-3678 253 8 http://www.sciencedirect.com/science/article/pii/s0021999118305527 http://www.sciencedirect.com/science/article/pii/s0021999118305527 PROPN