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The valuation of life contingencies: A symmetrical triangular fuzzy approximation

Author

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  • de Andrés-Sánchez, Jorge
  • González-Vila Puchades, Laura

Abstract

This paper extends the framework for the valuation of life insurance policies and annuities by Andrés-Sánchez and González-Vila (2012, 2014) in two ways. First we allow various uncertain magnitudes to be estimated by means of fuzzy numbers. This applies not only to interest rates but also to the amounts to be paid out by the insurance company. Second, the use of symmetrical triangular fuzzy numbers allows us to obtain expressions for the pricing of life contingencies and their variability that are closely linked to standard financial and actuarial mathematics. Moreover, they are relatively straightforward to compute and understand from a standard actuarial point of view.

Suggested Citation

  • de Andrés-Sánchez, Jorge & González-Vila Puchades, Laura, 2017. "The valuation of life contingencies: A symmetrical triangular fuzzy approximation," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 83-94.
  • Handle: RePEc:eee:insuma:v:72:y:2017:i:c:p:83-94
    DOI: 10.1016/j.insmatheco.2016.11.002
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    References listed on IDEAS

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    1. Heberle, Jochen & Thomas, Anne, 2014. "Combining chain-ladder claims reserving with fuzzy numbers," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 96-104.
    2. Alegre, Antoni & Claramunt, M. Merce, 1995. "Allocation of solvency cost in group annuities: Actuarial principles and cooperative game theory," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 19-34, August.
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    5. Zmeskal, Zdenek, 2005. "Value at risk methodology under soft conditions approach (fuzzy-stochastic approach)," European Journal of Operational Research, Elsevier, vol. 161(2), pages 337-347, March.
    6. Huang, Tao & Zhao, Ruiqing & Tang, Wansheng, 2009. "Risk model with fuzzy random individual claim amount," European Journal of Operational Research, Elsevier, vol. 192(3), pages 879-890, February.
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    8. Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
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    More about this item

    Keywords

    Life contingency pricing; Fuzzy numbers; Expected interval and beta expected value of a fuzzy number; Fuzzy financial mathematics; Mathematical expectation and variance of a fuzzy random variable;

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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