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Fuzzy Insurance

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  • Lemaire, Jean

Abstract

Fuzzy set theory is a recently developed field of mathematics, that introduces sets of objects whose boundaries are not sharply defined. Whereas in ordinary Boolean algebra an element is either contained or not contained in a given set, in fuzzy set theory the transition between membership and non-membership is gradual. The theory aims at modelizing situations described in vague or imprecise terms, or situations that are too complex or ill-defined to be analysed by conventional methods. This paper aims at presenting the basic concepts of the theory in an insurance framework. First the basic definitions of fuzzy logic are presented, and applied to provide a flexible definition of a “preferred policyholder” in life insurance. Next, fuzzy decision-making procedures are illustrated by a reinsurance application, and the theory of fuzzy numbers is extended to define fuzzy insurance premiums.

Suggested Citation

  • Lemaire, Jean, 1990. "Fuzzy Insurance," ASTIN Bulletin, Cambridge University Press, vol. 20(1), pages 33-55, April.
    • Handle: RePEc:cup:astinb:v:20:y:1990:i:01:p:33-55_00
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    Cited by:

    1. Lai, Li-Hua, 2008. "An evaluation of fuzzy transportation underwriting systematic risk," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(9), pages 1231-1237, November.
    2. Shapiro, Arnold F., 2013. "Modeling future lifetime as a fuzzy random variable," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 864-870.
    3. Arnold Shapiro, 2013. "Fuzzy post-retirement financial concepts: an exploratory study," METRON, Springer;Sapienza Università di Roma, vol. 71(3), pages 261-278, November.
    4. 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.
    5. Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
    6. Berry-Stölzle, Thomas R. & Koissi, Marie-Claire & Shapiro, Arnold F., 2010. "Detecting fuzzy relationships in regression models: The case of insurer solvency surveillance in Germany," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 554-567, June.
    7. Rosaria Simonelli, Maria, 2001. "Fuzziness in valuing financial instruments by certainty equivalents," European Journal of Operational Research, Elsevier, vol. 135(2), pages 296-302, December.
    8. Shapiro, Arnold F., 2002. "The merging of neural networks, fuzzy logic, and genetic algorithms," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 115-131, August.
    9. Tank, Fatih & Gebizlioglu, Omer L. & Apaydin, Aysen, 2006. "Determination of dependency parameter in joint distribution of dependent risks by fuzzy approach," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 189-194, February.
    10. Koissi, Marie-Claire & Shapiro, Arnold F., 2006. "Fuzzy formulation of the Lee-Carter model for mortality forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 287-309, December.
    11. de Andres Sanchez, Jorge & Terceno Gomez, Antonio, 2004. "Estimating a fuzzy term structure of interest rates using fuzzy regression techniques," European Journal of Operational Research, Elsevier, vol. 154(3), pages 804-818, May.
    12. Daniela Ungureanu & Raluca Vernic, 2015. "On a fuzzy cash flow model with insurance applications," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 39-54, April.
    13. Heberle, Jochen & Thomas, Anne, 2014. "Combining chain-ladder claims reserving with fuzzy numbers," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 96-104.
    14. 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.
    15. Shapiro, Arnold F. & Paul Gorman, R., 2000. "Implementing adaptive nonlinear models," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 289-307, May.
    16. Narayanaswamy, Pradeep & Bector, C. R. & Rajamani, Divakar, 1996. "Fuzzy logic concepts applied to machine--component matrix formation in cellular manufacturing," European Journal of Operational Research, Elsevier, vol. 93(1), pages 88-97, August.
    17. Yao, Kai & Qin, Zhongfeng, 2015. "A modified insurance risk process with uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 227-233.

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