TECHNIQUE FOR ASSESSING RELIABILITY OF INSURANCE COMPANIES Irina Voronova Rigas Technical University, Kalku str. 1, LV-1658 Riga, Latvia E-mail: irina.voronova@rtu.lv Received 18 November 2010; accepted 15 January 2011 Abstract. The purpose of this study is to improve the research technique for as- sessing the reliability of non-life insurance companies’ position. In this study, the author considers problems of assessment of reliability of insurance companies’ position. The author analyses indicators enabling to make complex assessment of insurance companies’ reliability. A technique of creating an integral indicator by using different methods of determining weighting rates of ratios validity is offered. Practical example of using an integral indicator of reliability of Latvian non-life insurance companies on the basis of public information is introduced. Rating is a risk indicator for potential consumers of insurance services. The offered technique may serve as an instrument for analysis of the reserves for enhancing reliability and competitiveness of insurance companies. Keywords: composite indices method, methods of reliability, insurance company, fuzzy set. Reference to this paper should be made as follows: Voronova, I. 2011. Technique for assessing reliability of insurance companies, Business, Management and Education 9(2): 295–309. http://dx.doi.org/10.3846/bme.2011.20 JEL classification: G22, G24. 1. Introduction At present, there exist a number of various techniques for assessing the reliability of institutions (insurance companies, banks, enterprises): rating assessment, point assess- ment of reliability and financial state, techniques of bankruptcy probability. As a rule, most techniques of rating assessment rely on public and internal information. Special agencies are granting ratings. In her works (Voronova, Pettere 2008, 2010), the author studied the development of rating approach to the assessment of reliability of Latvian insurance companies. The author investigates the possibility to use the technique of creating integral indicator of reliability in order to assess reliability of insurance com- panies. This technique has a scientific and practical interest. The conducted research was based on information comprised of indicators that describe activities of non-life insurance companies in Latvia. These indicators can be defined only by availability of B U S I N E S S, MA N AG E M E N T A N D E D U C AT I O N ISSN 2029-7491 print / ISSN 2029-6169 online 2011, 9(2): 295–309 http://dx.doi.org/10.3846/bme.2011.20 Copyright © 2011 Vilniaus Gediminas Technical University (VGTU) Press Technika www.bme.vgtu.lt 296 I. Voronova. Technique for assessing reliability of insurance companies public information. In 2010, there were 9 companies in the non-life insurance market, which conformed to Solvency I criteria by 31 December 2009. Unlike other participants of the financial market, assessment reliability of insur- ance companies is connected with the probability character of activities undertaken by insurance companies. Discussion on the criteria of insurance companies’ comparison is combined with the problem of determing the ability of an insurance company to meet all of the obligations to indemnify the insured. Rating is the function of risk manage- ment for service users. In its turn, insurance companies’ rating is a marketing function. 2. Methods of determining weighting ratios referring to the assessment of economic objects Methods of determining weighting ratios referring to the assessment of economic object has a history of development dating back more than a century. The method of creating “a for- mula of comparative assessment of projects” as one of the first variants of the technique of composite indicators was mentioned in 1908, when Krilov stated his “considerations about drawing up a formula of comparative assessment” for a battleship project taking part in an international competition (Hovanov 2005). Long years of history of practical application of the composite indices method demonstrated its universality. Universality of composite indices method is connected with the widespread general idea of scalar and vector assess- ment of complex objects in different branches of science. The composite indices method (CIM) (Hovanov 2009) demonstrated its universality. Universality of composite indices method is connected with the widespread general idea of scalarizations of vectorial criterion of complex objects in different branches of science. CIM method is also used to assess consumers’ interest in benefits. CIM and randomize aggregative indices method (Mikhaylov 2007) are applied in the theory of economic indices enabling to conduct multi-parametric assessment of different objects. For instance, in realization of the project Sustainability Index methodology in Latvia indices method is applied (Avena 2010). Sustainability Index methodology is the Latvian research product, however, it is based on corporate social responsibility theory as well as on the most notable global indices – Dow Jones Sustainability Index and Business in the Community made of Corporate Responsibility Index. Sustainability Index used in calculating the 93 questions in 5 sections – profile and strategy ( 1K ), the work environment ( 2K ), market relations ( 3K ), society ( 4K ) and the environment ( 5K ). Each section and each item have its own weight in the question section and a number of the criteria of sustainability, the role of the company overall assessment. For example, the criteria weights are the following: 1 2 30.1 , 0.35, 0.14,= = =K K K 4 0.15=K and 5 0.25K = . Among the techniques of developing integral indicators stand out applied stud- ies, based on the method of composite indicators or randomized composite indica- tors (Hovanov 2005, 2009; Mikoni 2009), which enable to develop scales of integral assessment of properties upon a greater number of criteria on the basis of existing 297 Business, Management and Education, 2011, 9(2): 295–309 classifications and common features. Multicriteria evaluation differs from the criteria and normalization technique of the initial data and has a very broad scope – from as- sessing the effectiveness of integrated financial-economic activities of enterprises in various industries (Ginevičius, Podvezko 2009, 2008a; Ginevičius, Zubrecovas 2009), the reliability of the credit institutions to measure the quality of training specialists in higher education (Mikhajlov 2007) to the evaluation of social phenomena (Ginevičius, Podvezko 2008b). The method of analytic hierarchy process (AHP) developed by T. Saaty (2005, 2008) can be used for calculations of integral indicator. The method presents information processing received by means of couple comparison of each level indicator fulfilled by experts. According to the method of hierarchies’ analysis it is sufficient to have range preference (priorities) assessments (better, worse, approximately, equal). There are vari- ous examples of the AHP method for assessing the risks of investment projects, such as construction (Ustinovichius et al. 2009). Determination of integral indicator may be produced by using the method of range correlation, allowing lying out objects of study in the increasing or decreasing order of any of their appropriate feature. To do this, it is necessary to correctly make receipt and processing of expert assessments. Complex assessment may be made on the basis of fuzzy descriptions (Doumpos, Zopounidis 2002; Nedosekin 2003a; Ahrameiko et al. 2004; Demidova 2009). For example, in the study by A. Nedosekin (2003b) for aggre- gating it is offered to use OWA-operator Jager (OWA – Ordered Weighted Averaging) (Yager 1993), moreover, Fushbern’s ratios serve as weights in convolution. There exist methods of calculating ratings which are based on the comparison of rated object on every financial-economic indicator with a standard object. In this case, the initial point for obtaining rating assessment is not subjective expert opinion, but established best results out of all combination of compared objects. Such methods as method of sums, method of sum places, method of geometrical average, method of distance (Taxometric method) and many other are used in different sources. Application of taxometric method for forming the reliability rating of insurance companies is con- sidered by the author (Voronova, Pettere 2010). Each of the mentioned methods has its advantages and disadvantages. Therefore there may exist many methods and it is not possible to determine, which is better and more objective than others as the used method is related to the aim of its user. 3. Choice of indicators for assessing reliability of insurance companies There exist a number of indicators characterizing the activities of insurance companies. The choice of indicators depends on the purposes of assessment. To select indicators it is neces- sary to meet the following two requirements: to calculate indicators only public information must be used and there should be absence of linear interdependence of ratios. The first requirement refers to the fact that many specialized indicators on the state of an insurance 298 I. Voronova. Technique for assessing reliability of insurance companies company require information not available in public. If the latter requirement is not met, assessment of reliability based on adequate convolution provides an incorrect result. Analysing 120 literary sources in Latvian and English the author selected 64 finan- cial indicators and drew up a table of the frequency. In conducting analysis financial indicators were divided into 9 groups: solvency indices, operative activity indices, prof- itability indices, leverage, liquidity indices, coverage ratio, cash flow ratio, different assets indices and other indices. Identified top 20 financial indicators used by insurance companies’ activities analysis are shown in Fig. 1. 80 70 60 50 40 30 20 10 0 Ca pit al ad eq ua cy Co mb ine d r ati o Lo ss ra tio Ex pe nc e r ati o Fin an cia l le ve ra ge Liq uid ity Re tur n o n e qu ity Ris k b as ed ca pit al ra tio Inv es tm en t r etu rn So lve nc y r ati o Ea rn ing s c ov er ag e r ati o Op er ati on al lev er ag e Ca sh flo w co ve ra ge ra tio Re tur n o n a ss ets De bt to tot al ca pit al ra tio Do ub le lev er ag e Un de rw rit ing le ve ra ge Ca pit ali za tio n r ati o La ps e r ati o Re tur n o n r ev en ue 67 58 54 49 36 36 33 29 23 23 17 16 13 11 10 10 8 7 6 6 N um be r of s ou rc e Fig. 1. Identified financial indicators of top 20 insurance companies’ activities analysis1 The author singled out the first group of indicators – solvency (F1), where were selected the most popular financial indicators characterizing operational efficiency (loss ratio and expense ratio), which occupy the third and the fourth place in popularity in the system of financial indicators as well as the indicator of investment efficiency (gross return rate of investments) (the ninth place in popularity), liquidity index (the sixth place) and reinsurance indicator (Fig. 1). The author refused to include combined ratio in the first group as there exists linear dependence between combined ratio and loss and expense ratios. In selecting indicators it is necessary to take into account the problem of deter- mining probability of an insurance company to meet all its obligations in insurance premiums that is why the author offered to single out the second group of indicators connected with insurance company ability to undertake risks (F2). This group contains indicators characterizing sufficiency of capital and reserve leverage. The third group of indicators characterizes insurance company competitiveness and commercial potential (F3). This group incorporates 4 indicators. Thus, the total number of indicators amounts to 13 and these indicators were grouped into 3 base groups. Key indicators of the tree of criteria of assessment of non life insurance companies’ reliability are given in the Fig. 2. 1 The study was conducted jointly with I. Gregore. The study materials used by international rating agencies – Stan- dard & Poor’s (ASV), Fitch Ratings (ASV), Moody’s Investors Service (ASV), AM Best (ASV) and other materials. 299 Business, Management and Education, 2011, 9(2): 295–309 F F1 F2 F3 F11 F12 F13 F14 F15 F21 F22 F23 F24 F31 F32 F33 F34 Fig. 2. Structure of indicators of assessment of non-life insurance companies’ reliability: F – selected factors of non-life insurance company reliability assessment; 1F – sol- vency; 2F – ability to undertake risks; 3F – competitiveness and commercial potential; 11F – loss ratio; 12F – expense ratio; 13F – liquidity ratio; 14F – rinsurance indicator; 15F – gross return rate of investments; 21F – company own capital over the minimum capital requirements by law; 22F – own capital over technical reserves; 23F – own capital over earned premiums; 24F – own capital over incurred claims; 31F – market share; 32F – gross premium growth rate; 33F – gross premium growth rate; 34F – re- serve adequacy ratio If any two predictors are perfectly correlated (correlation coefficient between any two predictors is greater than or equal 0.75), then there a multicollinearity problem may arise between predictors. Hence, it is not feasible to use closely correlated indicators in one model. Correlation analysis was done to see which factors are highly correlated to avoid multicollinearity problem. Table 1 shows obtained correlation matrix which is determined by using Pearson’s method. Given indicator, besides company own capital over incurred claims ( 24F ) refers to independent or poorly dependent indicators that are proved by conducted correlated analysis (Table 1). Thus, to draw up complex indicator of reliability the author left only 12 indicators (Table 2). Table 1. Correlation matrix 11F 12F 13F 14F 15F 21F 22F 23F 24F 31F 32F 33F 34F 11F 1.00 12F 0.68 1.00 13F –0.45 –0.83 1.00 14F –0.17 0.513 –0.684 1.00 15F 0.60 0.76 –0.77 0.43 1.00 21F –0.31 –0.64 0.62 –0.62 –0.55 1.00 300 I. Voronova. Technique for assessing reliability of insurance companies 11F 12F 13F 14F 15F 21F 22F 23F 24F 31F 32F 33F 34F 22F –0.27 –0.173 –0.186 0.166 0.06 –0.06 1.00 23F –0.61 –0.52 0.58 –0.01 –0.61 0.040 0.16 1.00 24F –0.71 –0.49 0.54 0.10 –0.59 0.04 0.16 0.98 1.00 31F –0.23 –0.41 0.34 –0.39 –0.29 0.18 –0.08 –0.04 0.00 1.00 32F 0.42 0.13 –0.031 –0.37 0.49 0.36 0.029 –0.47 –0.475 0.01 1.00 33F –0.55 –0.57 0.182 0.10 –0.52 0.34 0.26 0.21 0.20 0.21 –0.445 1.00 34F –0.33 –0.65 0.64 –0.42 –0.78 0.14 0.06 0.73 0.61 0.21 –0.553 0.38 1.00 4. Defining weighting ratios of complex assessment of non life insurance companies reliability Complex indicator (CI) of insurance company reliability assessment is found by double convolution according to the formula 1 1 , = = = β α∑ ∑ n m i ij j i j CI R (1) where: – indicator; βi – weight i of the group of base indicators; αij – weight j of indicators within the framework of the group of base indicators. Each group of base indicators and each indicator within the group are assessed ac- cording to their usefulness, then a system of weights for base n group indicators and every indicator ( jR ) within the framework of base groups is drawn up so that 1 1, 0, 1,..., , =  β =  β ≥ = ∑ n i j i i n and 1 1, 0, 1,..., , =  α =  α ≥ = ∑ m ij j ij j m (2) where: n – a number of base groups ( 3)=n (Fig. 2), m – a number indicator within the group. A calculation of complex assessment according to the groups of base indicators, in the author’s option, enables to arrange insurance company not only on the aggregate of indicators, but also on each of the groups of base indicators. Such an approach of complex assessment is likely to find out reserves of increasing reliability and competi- tiveness as well as direct management decisions on improving those parameters, where competitors have advantages. Continued Table 1 301 Business, Management and Education, 2011, 9(2): 295–309 Let us consider different ways of finding weighting ratios, received by ranging groups and indicators within the framework of groups. If all base groups and indicators in groups have equal usefulness, then weights of base groups and indicators within the framework of the group of base indicators are determined according to the formulae: 1 , β =i n and 1 , α =ij m (3) where: n – a number of base groups indicators; m – a number of indicators in each of base groups indicators. In the case when there exists a system of preferences base groups and indicators in a group are ranged according to the descending of usefulness. In this case to determine base group weights and indicators in a group it is recommended to use Fishburn’s scale (Baron, Barrett 1996; Potapov, Evstafjeva 2008): 2( 1) , ( 1)j n i n n − + β = + and 2( 1) ( 1) − + α = +ij m j m m , (4) where: i, j – the number of current base group and the number of indicators within the framework of every base groups. To determine weighting ratios may be principle of fuzzy descriptions. The function [ ]j : 0,1] [0,1]→ meets j(0) 0= and j(1) 1= . Weighting ratios are determined by the formula 1 1 j( ) j( ), 1,..., , − α = − =i i i n n n (5) where: i – the number of indicator; n – a number of indicators. One may choose any function, for example polynomial of second order: 2j( ) = + +x ax bx c. As j(0) 0= , then 0=c . 5. Sample evaluation reliability of non life insurance companies The study was carried out based on 10 Latvian non life insurance companies. In her research the author used the available data for 2009 year. Initial data for assessing reliability of insurance companies are given in Table 2. To create weighting systems 3 experts were enquired. To avoid overloading the study with mathematic calculations, let us suppose that expert opinions are agreed upon to a certain degree. The study introduces calculations of weighting rations only by 2 methods: by using Fishburn’s technique and fuzzy cluster. If the significance of both basic groups of indicators and indices in the groups are equivalent, then the formula (3) weights of basic groups ( βi ) in this case is – 0.333, but weighting ratios of the first core group 1 0.2α =j , for the second performance 302 I. Voronova. Technique for assessing reliability of insurance companies 2 1 3α =j and third groups are 3 0.25α =i . Using formula (4), for example, basic groups 1 2 3> >F F F we have weights for each of the basic groups 1 1 2 2 3 3 2(3 1 1) : 0.5, 3(3 1) 2(3 2 1) 1 : 0.333, 3(3 1) 3 2(3 3 1) : 0.167. 3(3 1) F F F − + β = = + − + β = = = + − + β = = + System of weighting ratio for the first base group indicators having preferences 11 12 13 14 15> > > >F F F F F is 11 12 13 140.333; 0.267; 0.2; 0.133α = α = α = α = and 15 0.067α = . System of weighting ratio for the second base group indicators having pref- erences 21 22 23F F F> > is 22 230.333; 0.1667.α = α = System of weighting ra- tio for the third base group indicators having preferences 31 32 33 34F F F F> > > is 31 32 33 340.4; 0.3; 0.2; 0.1α = α = α = α = . Table 2. Investigated insurances’ companies 2009 indicator matrix (example)* Factors Insurance company code 1 2 3 4 5 6 7 8 9 10 F1 Insurance company solvency F11 0.534 0.459 0.574 0.711 0.637 0.547 0.612 0.537 1.092 0.610 F12 0.402 0.515 0.434 0.526 0.322 0.328 0.315 0.324 0.672 0.347 F13 1.284 0.854 0.530 0.331 1.535 1.394 1.377 1.732 0.552 1.384 F14 0.015 0.500 0.304 0.361 0.029 0.021 0.007 0.079 0.087 0.059 F15 3.865 8.681 8.547 7.486 4.487 5.350 7.274 2.186 11.441 7.195 F2 Insurance company ability to undertake risks F21 11.100 1.513 2.699 1.190 10.194 4.034 12.166 4.947 0.666 2.977 F22 0.727 0.473 2.699 0.348 0.533 0.681 0.736 0.835 0.320 0.762 F23 0.484 0.649 0.546 0.391 0.426 0.563 0.554 1.082 0.262 0.601 F24 ** 0.905 1.412 0.950 0.550 0.669 1.029 0.906 2.016 0.240 0.986 F3 Insurance company competitiveness and commercial potential F31 0.205 0.040 0.064 0.043 0.236 1.029 0.224 0.051 0.025 0.045 F32 –0.315 –0.388 –0.312 –0.589 –0.339 –0.388 –0.003 –0.579 –0.086 –0.362 F33 11.000 11.000 14.000 15.000 16.000 13.000 13.000 13.000 6.000 10.000 F34 1.27 0.98 1.26 1.34 1.38 1.53 1.26 1.98 1.03 1.47 *Calculated by the author on the basis of the given financial statements on 2009 available on the home page of insurance companies – Balta, BAN, RSK, Balticums, BTA, If, ErgoLatvija, Gjensidiga and SEESAM **Excluded from drawing up complex indicator of insurance companies reliability 303 Business, Management and Education, 2011, 9(2): 295–309 To draw up a system of weighting ratios 3 experts are used. Total weighting ratio is calculated as a mean arithmetic of weights, determined by experts. There were no dif- ference in opinions on ranging indicators of base groups and indicators of the first and third groups. As for preferences of the third group of indicators, there were distinctions, which are summed up in Table 3. Table 3. Meaning of weighting ratios and their mean values for third base group indicators Expert 31 F – Market share 32F – Gross premium growth rate 33F – Portfolio diversification 34F – Reserve adequacy ratio First 0.4 0.3 0.2 0.1 Second 0.4 0.3 0.1 0.2 Third 0.4 0.2 0.1 0.3 Mean value 0.4 0.267 0.133 0.2 As for preferences, let us consider determination of weighting ratios by using the principle fuzzy cluster for base groups of indicators. By formula (5) we have: 1 2 3 1j( ),3 2 1j( ) j( ),3 3 3 2j( ) ( ).3 3 β =  β = −  β = − ϕ (6) Let us take that 1( ) 0, 53φ = , which corresponds to the firts weight ratio calculated on the Fishburn’s formula. As a 2( )φ = + +x ax bx c and 0=c , we have ( ) 21 11j( ) ( ) 0.5,33 3 9 3 1 1. a b a b a b  = ⋅ + ⋅ = + =  ϕ = + + (7) From (7) find 0.75, 1.75= − =a b . Thus, as a result 1( ) 0.5.3φ = Let us calculate weight- ing ratios for the rest base groups 2 3 2 1 4 2( ) ( ) 0.75 1.75 0.5 0.83334 0.5 0.33334,3 3 9 3 1(1) ( ) 1 0.83334 0.16666.3 β = φ − φ = − ⋅ + ⋅ − = − = β = φ − φ = − = A determined quantity of weight ratios coincided with the meanings calculated ac- cording to Fishburn’s technique. Weights of each base group determined by the four methods are presented in Table 4, column “Weight of base groups of indicators”, which is divided into four parts: on the left – all base groups have equal meaning, in the mid- dle – base groups are strictly ranged, weights are determined by Fishburn’s technique, on the right – weights of base groups are assessed with a view to expert opinions, and on the last – on the basis of fuzzy cluster principle. 304 I. Voronova. Technique for assessing reliability of insurance companies Table 4. Comparison of weighting ratios of base groups C od e Name of base groups Weight of base groups of indicatorsβi F1 Insurance company solvency 0.334 0.5 0.5 0.5 F2 Insurance company liability to undertake risks 0.333 0.333 0.333 0.333 F3 Insurance company competitiveness and commercial potential 0.333 0.167 0.167 0.167 Similarly, we define weights for each of the basic groups. The results are the fol- lowing: 11 12 13 14 150.334; 0.266; 0.2; 0.134; 0.066,α = α = α = α = α = 21 22 230.416; 0.334; 0.25.α = α = α = The calculations provide evidence of some difference in the weights only in the second subgroup. Based on these weights and the initial data (Table 2), a comprehen- sive indicator of reliability of the insurance company is determined according to the formula (2). Example of calculating the complex index of reliability for the insurance companies’ initial data for 2009 is given in Table 5. Table 5. Example of calculating the complex index of reliability of non life insurance companies (2009, Fishburn’s technique) Factors Weight inindi- cator Insurance company code 1 2 3 4 5 6 7 8 9 10 F1 0.500 0.401 0.553 0.525 0.495 0.454 0.454 0.524 0.384 0.714 0.530 F11 0.333 0.178 0.153 0.191 0.237 0.212 0.182 0.204 0.179 0.364 0.203 F12 0.267 0.107 0.137 0.141 0.140 0.086 0.087 0.084 0.086 0.179 0.092 F13 0.200 0.257 0.171 0.106 0.066 0.307 0.279 0.275 0.346 0.110 0.277 F14 0.133 0.002 0.067 0.041 0.048 0.004 0.003 0.001 0.010 0.012 0.008 F15 0.067 0.258 0.579 0.570 0.499 0.299 0.357 0.485 0.146 0.763 0.480 Total F1 1.000 0.802 1.107 1.049 0.991 0.908 0.908 1.049 0.768 1.428 1.060 F2 0.333 1.958 0.341 0.541 0.258 1.782 0.779 2.140 0.977 0.161 0.614 F21 0.500 5.551 0.757 1.350 0.593 5.097 2.017 6.083 2.473 0.333 1.489 F22 0.333 0.242 0.158 0.182 0.116 0.178 0.227 0.245 0.278 0.107 0.254 F23 0.167 0.081 0.108 0.091 0.065 0.071 0.094 0.092 0.180 0.044 0.100 Total F2 1.000 5.874 1.023 1.622 0.774 5.346 2.338 6.420 2.932 0.483 1.843 F3 0.167 0.224 0.199 0.264 0.268 0.312 0.253 0.274 0.257 0.132 0.201 F31 0.400 0.082 0.016 0.026 0.017 0.094 0.026 0.089 0.020 0.010 0.018 F32 0.300 –0.094 –0.117 –0.094 –0.177 –0.102 –0.116 –0.001 –0.174 –0.026 –0.11 F33 0.100 1.100 1.100 1.400 1.500 1.600 1.300 1.300 1.300 0.600 1.000 F34 0.200 0.255 0.195 0.251 0.268 0.277 0.306 0.253 0.397 0.206 0.294 Total F3 1.000 1.342 1.195 1.583 1.609 1.870 1.516 1.641 1.543 0.791 1.204 CI total 2.583 1.093 1.329 1.021 2.547 1.486 2.938 1.619 1.007 1.345 305 Business, Management and Education, 2011, 9(2): 295–309 In order to divide insurance categories according to a certain scale (Table 6), the author investigates mathematical approach, taking into account that all insurance compa- nies, which have obtained points over the first quartile, could be considered as high reli- ability company, between the first quartile and the third quartile could be considered as a moderate reliability company, but which are below the third quartile – as low reliability company (Voronova, Pettere 2010). The results of determining the complex index of the reliability of insurance companies using the weights found on the basis of Fishburn’s technique and based on the fuzzy description shows full match results. In the dynamics of a composite index of insurance companies shows that they belong to the stable grade. Table 6. Insurance company reliability assessment scale 2008 2009 weights determined using weights determined using Fishburn’s technique fuzzy description Fishburn’s technique fuzzy description Code Obtained assessment Code Obtained assessment Code Obtained assessment Code Obtained assessment 7 2.709 7 2.361 7 2.938 7 2.616 5 2.421 5 2.117 1 2.583 1 2.288 1 2.342 1 2.031 5 2.547 5 2.276 8 1.693 8 1.530 8 1.619 8 1.511 3 1.360 3 1.251 6 1.486 6 1.389 6 1.312 6 1.189 10 1.345 10 1.279 10 1.177 10 1.071 3 1.329 3 1.269 2 1.140 2 1.067 2 1.093 2 1.069 4 1.091 4 0.993 4 1.021 4 0.999 9 0.942 9 0.846 9 1.007 9 0.996 – high reliability; – moderate reliability; – low reliability Available movement of insurance companies in the second group of reliability is associated with a change in the group of indicators of their solvency. Having done a lot of research in the field of assessing insurance companies’ reliability the author con- siders that the results of the study fully conform to the obtained ranging of insurance companies according to complex indicator. 6. Conclusions Conducted analisis of some methods of integrated assessment of complex objects showed their versatility. The methods are not ideal, and the choice of this or that meth- od depends on the purpose of study, availability of information and competence of specialists. There is an extensive use of multicriteria evaluation in decision-making in economic and financial sphere and ratings of economic entities. The quality of draw- ing up the technique of integrated assessment of reliability to a great extent is large- ly determined by a quality selection of indicators included in the complex indicator. 306 I. Voronova. Technique for assessing reliability of insurance companies The selection of indicators was carried out using frequency analysis of the popularity of performance in financial analysis, insurance companies and the experience of inter- national rating agencies including restrictions on publicity of information sources and the absence of a linear mutual dependence. Selected indicators (except indicators of 2F ) are independent. As for indicators of the group “Insurance company solvency” it is necessary to carry out additional re- search in order to find the best combination of indicators with weakly dependent parameters. Let us consider two methods of calculating the weighting ratios to assess reliability of insurance companies – on a Fishbur’s technique and using the principle of a fuzzy description. Calculated ratios for methods have some drawbacks. Fishburn’s technique has dependence on the number of indicators for whose weighting ratios are determined and the character of indicators is not taken into account. If exspert opin- ions are used for creating Fishburn’s technique the competence of the experts should be up to standards. By using the method of fuzzy descriptions, the results fully depend on a selected function. Though in this research the function was randomly chosen, the results practi- cally did not differ from those received by using Fishburn’s technique. A practical example of using complex assessment of reliability showed an opportu- nity to carry out assessment of insurance companies’ reliability basing on public infor- mation. Availability of double convolution in the technique enables to study additionally the reserves of increasing reliability and competitiveness of the insurance company. This technique helps to direct management improvement of those insurance company parameters where competitors have advantage. References Ahrameiko, A. A.; Berbasova, N. Y.; Siniavskaya, O. A.; Zhelezko, B. A. 2004. Methodology of the Estimation of Quality of Objects with Complex Structure under Conditions of Non-Stochastic Uncertainty, in International Conference on Fuzzy Sets and Soft Computing in Economics and Finance, Saint- Petersburg, Russia, 17–20 June 2004. Proceedings. Saint-Petersburg, 360–367. ISBN 968-389-030-3. Annual Accounts. AAS Balta [online], [cited 12 July 2010]. Available from Internet: . AAS Gjensidigen Baltic. Financial statements. For the year ended 31 December 2009 [online], [cited 10 July 2010]. Available from Internet: . Apdrošināšana Baltikums. 2009. Gada pārskats [online], [cited 10 July 2010]. Available from Internet: . Avena, D. 2010. Kas ir ilgtspējas indekss?, in Ilgtspējas indekss 2010 [cited 12 July 2010]. Available from Internet: . Baron, H. F.; Barrett, B. E. 1996. Decision quality using ranked attribute weights, Management Science 42(11): 1515–1523. doi:10.1287/mnsc.42.11.1515 http://www.balta.lv/public/26103hp http://www.balta.lv/public/26103hp http://www.gjensidige.lv/images/pdfs/lv/Finansu_atskaites/ http://www.seb.lv/data/product_documentsin dekss_1-24.pdf http://dx.doi.org/10.1287/mnsc.42.11.1515 307 Business, Management and Education, 2011, 9(2): 295–309 Berg, J. S. 2006. Moody’s Global Rating Methodology for Property and Casualty Insurers. Moody’s Investors Service. – Moody’s Investors Service, Inc., 28 p. [cited 14 April 2010]. Available from Internet: . Best, A. M. 2007. An Explanation of Best’s Rating System and Procedures: Property / Casualty A. M. Best Company. – A. M. Best Company, Inc. [cited 14 April 2010]. Available from Internet: . BTA AAS. Annual report for 2009 [online], [cited 12 July 2010]. Available from Internet: . Demidova, L. A. 2009. Razvitie metodov nechiotkikh mnozhestv i geneticheskikh algoritmov dlia zadach podderzhki priniatiia reshenii v usloviiakh neopredelennosti. Ph. Dissertation, Ryazan [cited 20 October 2010]. Available from Internet: . Doumpos, M.; Zopounidis, C. 2002. Multicriteria decision aid classifications methods. Springer. 268 p. ISBN 978-1-40200805-4. Fitch Ratings: Rejtingi kompanij po strakhovanuiiju inomu, chem strakhovanie zhizni (Mezhdunarodnaja metodoloģija). 2007. “Fitch Ratings” v Rossii. New York: Fitch Inc., Fitch Ratings, Ltd. [cited 14 April 2010]. Available from Internet: . Gada finanšu pārskati ERGO Latvija AAS [online], [cited 12 July 2010]. Available from Internet: . Gada pārskati. Baltijas apdrošināšanas nams (BAN) [online], [cited 12 July 2010]. Available from Internet :. Ginevičius, R.; Podvezko, V. 2008a. Multicriteria graphical-analytical evaluations of the financial state of construction enterprisies, Technological and Economic Development of Economy 14(4): 452–461. doi:10.3846/1392-8619.2008.14.452-461 Ginevičius, R.; Podvezko, V. 2008b. A feasibility study of multicriteria methods application to quantita- tive evaluation of social phenomena, Verslas: teorija ir praktika [Business: Theory and Practice] 9(2): 81–87. doi:10.3846/1648-0627.2008.9.81-87 Ginevičius, R.; Podvezko, V. 2009. Evaluating the changes in economic and social development of Lithuanian counties by multiple criteria methods, Technological and Economic Development of Economy 15(3): 418–436. doi:10.3846/1392-8619.2009.15.418-436 Ginevičius, R.; Zubrecovas, V. 2009. Selection of optimal real estate investment project basing of mul- tiple criteria evaluation using stohastic dimensions, Journal of Business Economics and Management 10(3): 261–270. doi:10.3846/1611-1699.2009.10.261-270 Hovanov, N. V. 2005. Ocenka slozhnykh ekonomicheskikh ob’ektov i processov v usloviiakh neoprede- lennosti. К 95-letiiu metoda svodnykh pokazatelej A. N. Кrjlova, Vestnik SPbU. Serija 5. Vypusk 1: 138– 144 [cited 20 October 2010]. Available from Internet: . Hovanov, N. V. 2009. O postroenii reitinga rossiiskikh nauchnykh zhurnalov kak povod podumat ob obshchikh principakh primeneniia metoda svodnykh pokazatelej, UBS 27: 75–80 [cited 20 October 2010]. Available from Internet: . Kornilov, V. V.; Seregin, I. A.; Hovanov, N. V. 2000. Bayesovskaia model obrabotki nechislennoi, ne- tochnoi i nepollnoi informacii o vesovykh koefficientakh [online], [cited 20 October 2010]. Available from Internet: . http://www.ambest.com/rati ngs/ http://www.ambest.com/rati ngs/ http://www.rsreu.ru/component/op tion,com_docman/task,doc.../gid,736/> http://ww http://www.ergo.lv/lat/aboutus/latvia/offers/ http://www http://dx.doi.org/10.3846/1392-8619.2008.14.452-461 http://dx.doi.org/10.3846/1648-0627.2008.9.81-87 http://dx.doi.org/10.3846/1392-8619.2009.15.418-436 http://dx.doi.org/10.3846/1611-1699.2009.10.261-270 http://www.mathnet.ru/php/ 308 I. Voronova. Technique for assessing reliability of insurance companies Likvidējamas RSK apdrošināšanas AS 2009. Gada pārskats. 2009 [online], [cited 12 July 2010]. Available from Internet: . Mikhajlov, M. V. 2007. ASPID – metodoloģiia kak instrument izmereniia kachestva podgotovki spe- cialistov v vuze, Vestnik SPbU. Serija 5. Vypusk 3: 69–82 [cited 25 November 2010]. Available from Internet: . Mikoni, S. V. 2009. Mnogokriterialnyi vybor na konechnom mnozhestve alternativ. Saint-Petersburg: Lan. 272 p. ISBN 978-5-8114-0984-6. Nedosekin, A. 2003a. Fuzzy financial management [cited 12 July 2010]. Available from Internet: . Nedosekin, A. O. 2003b. Metodologicheskie osnovy modelirovaniia finansovoy dejatelnosti s ispolzo- vaniem nechetko-mnozhestvennykh opisanii: Ph. Dissertation. Saint-Petersburg: SPb Gos. Universitet. 280 р. Potapov, D. K.; Evstafjeva, V. V. 2008. O metodakh opredeleniia vesovykh koefficientov v zadache ocenki nadezhnosti kommercheskikh bankov, in Socialno-ekonomicheskoe polozhenie Rossii v novykh geopoliticheskikh i finansovo-ekonomicheskikh usloviiakh: realii i perspektivy razvitiia [cited 12 July 2010]. Saint-Petersburg, Institut biznesa i prava, 191–195. Available from Internet: . Saaty, T. 2008. Priniatie reshenii pri zavisimostiach b obratnyh svjazjah: analiticheskie seti. Moskva: LKI. 360 p. ISBN 978-5-382-00422. Saaty, T. L. 2005. Theory and Applications of the Analytic Network Process: Decision making with Benefits, Opportunities, Cost and Risk. RWS publication. 352 p. ISBN 1-888603-06-2. Standard & Poor’s: Insurance Ratings Criteria: Property. 2004. Casualty Edition / Standard & Poor’s, a Division of the McGraw-Hill Companies, Inc.: New York: The McGraw-Hill Companies, Inc. 149 p. Ustinovichius, L.; Barvidas, A.; Vishnevskaja, A.; Ashikhmin, U. 2009. Multicriteria verbal analysis for the dicision of construction problems, Tehnological and Economic Development of Economy 15(2): 326–340. doi:10/3846/1392-8619.2009.15.326-340 Voronova, I.; Pettere, G. 2008. Rating as an Assessment Instrument of the Insurance Market partici- pants Security, in 49th International Scientific Conference of Riga Technical University “The Problems of Development of National Economy and Enterpreneurship”: RTU Scientific Conference of Economics and Entrepreneurship (SCEE’2008). Conference Proceedings. Riga: RTU Publishing House, 163–165. Voronova, I.; Pettere, G. 2010. Rating of the Latvian insurance companies based of public information. International Congress of Actuaries ICA2010 [cited 12 July 2010]. Available from Internet: . Yager, R. R. 1993. Families of OWA operation. Fuzzy Sets and Systems [cited 12 July 2010]. Available from Internet: . http://www.rsk.lv/lv/cat/26/ http://author.econ.pu http://www.ibl.ru/konf 041208 /60.pdf http://www.ibl.ru/konf 041208 /60.pdf http://dx.doi.org/10/3846/1392-8619.2009.15.326-34 http://www.ica http://www.ica http://www.sciencedirect.com/science?ob=MImg&_imagekey=B6V05-48MYJPV -F9-1&cdi http://www.sciencedirect.com/science?ob=MImg&_imagekey=B6V05-48MYJPV -F9-1&cdi 309 Business, Management and Education, 2011, 9(2): 295–309 DRAUDIMO KOMPANIJŲ PATIKIMUMO ĮVERTINIMO METODIKA I. Voronova Santrauka Šio tyrimo tikslas yra pagerinti ne gyvybės draudimo kompanijų pozicijos patikimumo vertinimo tyrimų metodiką. Nagrinėjamos šių kompanijų pozicijos patikimumo vertinimo problemos, analizuo- jami rodikliai, sudarantys prielaidas atlikti kompleksinį draudimo kompanijų patikimumo vertinimą. Straipsnyje siūlomas sukurto integruotojo rodiklio metodas, naudojant skirtingus reikšmingumo nus- tatymo būdus, pateikiama Latvijos ne gyvybės draudimo kompanijų praktinių pavyzdžių ir remiamasi viešąja informacija. Reitingas yra draudimo paslaugų potencialių vartotojų rizikos rodiklis. Siūloma metodika gali būti naudinga priemonė draudimo kompanijų konkurencingumui didinti. Reikšminiai žodžiai: sudėtinių indeksų metodas, patikimumo metodai, draudimo kompanija, fuzzy metodas. Irina VORONOVA is Associated Professor of Investment and Financial Management at Faculty of Engineering Economics and Management of Riga Technical University. She holds a Doctor Degree in Economy of Latvian Academy of Sciences. She has thirty-five years of teaching practice in entre- preneurship and finance. Her academic publications include articles in the Journal of Business eco- nomics and Management (Vilnius), Scientific Proceedings of Riga Technical University, International Congress of Actuaries and others. She is the co-author of the first textbook of Risk Management in Latvian language. She is member of Boarder of Latvian Actuarial Association.