Calculating Insurance Claim Reserves with Hybrid Fuzzy Least Squares Regression Analysis

Year 2010, Volume: 23 Issue: 2, 163 - 170, 30.03.2010

Furkan Baser Aysen Apaydın

Abstract

The prediction of an adequate amount of claim reserves is of the greatest importance to face the responsibilities assumed by an insurance company. Although many different deterministic and stochastic methods based on statistical analyses are used for claims analysis, presence of many internal and external factors that increase the uncertainty in insurance environment may lead to considerable loss in reliability of statistical methods. Therefore, in a state of uncertainty that exist in the nature of many actuarial and financial problems, when convenient and reliable data is not held, the use of fuzzy set theory becomes very attractive to get more actual results. In this paper, a method for calculating insurance claim reserves using hybrid fuzzy least-squares regression analysis is proposed. The results from classical method and this soft computing approach are compared by using original data in automobile liability insurance.

 

 Key Words: Insurance, Claims reserving, Fuzzy numbers, Fuzzy arithmetic, Fuzzy regression.

 

Keywords

Insurance, Claims reserving, Fuzzy numbers, Fuzzy arithmetic, Fuzzy regression

References

• Aliev, R.A., Fazlollahi, B., Aliev, R.R., “Soft Computing and its Applications in Business and Economics”, Springer-Verlag, New York, 80 – 81 (2003).
• Andrés, J.de, Terceño, A., “Applications of fuzzy regression in actuarial analysis”, Journal of Risk and Insurance, 70(4): 665–699 (2003).
• Benjamin, S., Eagles, L.M., “Reserves in Lloyd’s and the London market”, Journal of the Institute of Actuaries, 113(2): 197–257 (1986).
• Boulter,A., Grubbs, D., “Late Claims Reserves in Reinsurance”, Swiss Re Press, Zurich, 5-28 (2000).
• Buckley, J.J., “Fuzzy Probability and Statistics”, Springer-Verlag, New York, 171-195 (2006).
• Chang, Y.-H.O., Ayyub, B.M., “Fuzzy regression methods – a comparative assessment”, Fuzzy Sets and Systems, 119(2): 187–203 (2001).
• Chang, Y.-H.O., “Hybrid fuzzy least-squares regression analysis and its reliability measures”, Fuzzy Sets and Systems, 119(2): 225–246 (2001).
• Dubois, D., Prade, H., “Fuzzy Sets for Intelligent Systems”, Morgan Kaufmann Publishers, San Francisco, CA, 45-61 (1993).
• Goovaerts, M.J., Kaas, R., Heerwaarden, A.E., Bauwelinckx, T., “Effective Actuarial Methods”, North-Holland, Amsterdam, 243-252 (1990).
• Hossack, I.B., Pollard, J.H., Zehnwirth, B., “Introductory Statistics with Applications in General Insurance”, Cambridge University Press, Cambridge, 206-242 (1999).
• Kaufmann, A., Gupta, M.M., “Introduction to Fuzzy Arithmetic: Theory and Applications”, Van Nostrand Reinhold, New York, 9-42 (1991).
• Moskowitz, H., Kim, K., “On assessing the H value in fuzzy linear regression”, Fuzzy Sets and Systems, 58: 303–327 (1993).
• Shapiro, A.F., “Fuzzy logic in insurance”, Insurance: Mathematics and Economics, 35(2): 399–424 (2004). [14] Shapiro, A.F., “Fuzzy random variables”. Insurance: Mathematics and Economics, 44(2): 307–314 (2009).
• Straub, E., “Non-life Insurance Mathematics”, Springer-Verlag, Berlin, 102-115 (1997).
• Tanaka, H., “Fuzzy data analysis by possibilistic linear models”, Fuzzy Sets and Systems, 24: 363– 375 (1987).
• Taylor, G., “Separation of inflation and other effects from the distribution of non-life insurance claim delays”, Astin Bulletin, 10(1): 217–230 (1977).
• Verbeek, H.G., “An approach to the analysis of claims experience in motor liability excess of loss reassurance”, Astin Bulletin, 6: 195–202 (1972).
• Zadeh, L.A., “The roles of fuzzy logic and soft computing in the conception, design and deployment Technology Journal, 14(4): 32-36 (1996). systems”, BT