Hybrid fuzzy least-squares regression analysis in claims reserving with geometric separation method
Claims reserving is obviously necessary for representing future obligations of an insurance company and selection of an accurate method is a major component of the overall claims reserving process. However, the wide range of unquantifiable factors which increase the uncertainty should be considered when using any method to estimate the amount of outstanding claims based on past data. Unlike traditional methods in claims analysis, fuzzy set approaches can tolerate imprecision and uncertainty without loss of performance and effectiveness. In this paper, hybrid fuzzy least-squares regression, which is proposed by Chang (2001), is used to predict future claim costs by utilizing the concept of a geometric separation method. We use probabilistic confidence limits for designing triangular fuzzy numbers. Thus, it allows us to reflect variability measures contained in a data set in the prediction of future claim costs. We also propose weighted functions of fuzzy numbers as a defuzzification procedure in order to transform estimated fuzzy claim costs into a crisp real equivalent.
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- Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
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- Wu, Hsien-Chung, 2003. "Fuzzy estimates of regression parameters in linear regression models for imprecise input and output data," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 203-217, February.
- de Andres-Sanchez, Jorge, 2007. "Claim reserving with fuzzy regression and Taylor's geometric separation method," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 145-163, January.
- Paulo J. R. Pinheiro & Jo�o Manuel Andrade e Silva & Maria de Lourdes Centeno, 2003. "Bootstrap Methodology in Claim Reserving," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 701-714.
- Jorge de Andrés Sánchez & Antonio Terceño Gómez, 2003. "Applications of Fuzzy Regression in Actuarial Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 665-699.
- Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
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