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Combining chain-ladder claims reserving with fuzzy numbers

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  • Heberle, Jochen
  • Thomas, Anne

Abstract

In this paper we extend the classical chain-ladder claims reserving method using fuzzy methods. Therefore, we derive new estimators for the claims development factors as well as new predictors for the ultimate claims. The advantage in using fuzzy numbers lies in the fact that the model uncertainty is directly included in and can be controlled by the “new” fuzzy claims development factors. We also provide an estimator for the uncertainty of the ultimate claims for single accident years and for aggregated accident years.

Suggested Citation

  • Heberle, Jochen & Thomas, Anne, 2014. "Combining chain-ladder claims reserving with fuzzy numbers," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 96-104.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:96-104
    DOI: 10.1016/j.insmatheco.2014.01.002
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    References listed on IDEAS

    as
    1. Apaydin, Aysen & Baser, Furkan, 2010. "Hybrid fuzzy least-squares regression analysis in claims reserving with geometric separation method," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 113-122, October.
    2. Peters, Gareth W. & Wüthrich, Mario V. & Shevchenko, Pavel V., 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 36-51, August.
    3. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    4. de Wit, G. W., 1982. "Underwriting and uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 1(4), pages 277-285, October.
    5. Gisler, Alois & Wüthrich, Mario V., 2008. "Credibility for the Chain Ladder Reserving Method," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 565-600, November.
    6. 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, December.
    7. Lemaire, Jean, 1990. "Fuzzy Insurance," ASTIN Bulletin, Cambridge University Press, vol. 20(1), pages 33-55, April.
    8. 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.
    9. Gareth W. Peters & Mario V. Wuthrich & Pavel V. Shevchenko, 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Papers 1004.2548, arXiv.org.
    10. Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
    11. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, September.
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    Cited by:

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    3. 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.

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    More about this item

    Keywords

    Claims reserving; Chain-ladder model; Fuzzy numbers; Ultimate claims predictor; Fuzzy uncertainty;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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