Claim reserving with fuzzy regression and Taylor’s geometric separation method

Abstract

Claim provisions are crucial for the financial stability of insurance companies. This is why actuarial literature has proposed several claim reserving methods, which are usually based on statistical concepts. However, the mutant and uncertain behaviour of insurance environments does not make it advisable to use a wide database when calculating claim reserves, and so it in fact makes the use of Fuzzy Set Theory very attractive. This paper develops a claim reserving method that combines Ishibuchi and Nii’s extension [Ishibuchi, H., Nii, M., 2001. Fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks. Fuzzy Sets and Systems 119, 273–290] to the fuzzy regression methods described by Tanaka et al. [Tanaka, H., Uejima, S., Asai, K., 1982. Linear regression analysis with fuzzy model. IEEE Trans. Man Cybernetics 41, 389–396], Tanaka [Tanaka, H., 1987. Fuzzy data analysis by possibilistic linear models. Fuzzy Sets and Systems 24, 363–375], Savic and Pedrycz [Savic, D., Predrycz, W., 1992. Fuzzy linear models: construction and evaluation. In: Fuzzy Regression Analysis. Physica-Verlag, Heidelberg, pp. 91–100] and Tanaka and Ishibuchi (1992) [Tanaka, H., Ishibuchi, H., 1992. A possibilistic regression analysis based on linear programming. In: Fuzzy Regression Analysis. Physica-Verlag, Heidelberg, pp. 47–60] with the scheme for claim reserving proposed by Taylor (1978) [Taylor, G., 1978. Statistical testing of a non-life insurance run-off model. In: Proceedings of the First Meeting of the Contact Group Actuarial Sciences, pp. 37–64].