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Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method

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  • Jorge De Andrés-Sánchez

    (Social and Business Research Laboratory, Universitat Rovira i Virgili, Campus de Bellissens, 43204 Reus, Spain)

Abstract

Estimating loss reserves is a crucial activity for non-life insurance companies. It involves adjusting the expected evolution of claims over different periods of active policies and their fluctuations. The chain-ladder (CL) technique is recognized as one of the most effective methods for calculating claim reserves in this context. It has become a benchmark within the insurance sector for predicting loss reserves and has been adapted to estimate variability margins. This variability has been addressed through both stochastic and possibilistic analyses. This study adopts the latter approach, proposing the use of the CL framework combined with intuitionistic fuzzy numbers (IFNs). While modeling with fuzzy numbers (FNs) introduces only epistemic uncertainty, employing IFNs allows for the representation of bipolar data regarding the feasible and infeasible values of loss reserves. In short, this paper presents an extension of the chain-ladder technique that estimates the parameters governing claim development through intuitionistic fuzzy regression, such as symmetric triangular IFNs. Additionally, it compares the results obtained with this method with those derived from the stochastic chain ladder by England and Verrall.

Suggested Citation

  • Jorge De Andrés-Sánchez, 2024. "Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method," Mathematics, MDPI, vol. 12(6), pages 1-24, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:845-:d:1356435
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    References listed on IDEAS

    as
    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. Silvia Muzzioli & Luca Gambarelli & Bernard Baets, 2020. "Option implied moments obtained through fuzzy regression," Fuzzy Optimization and Decision Making, Springer, vol. 19(2), pages 211-238, June.
    3. Oleg Uzhga-Rebrov & Peter Grabusts, 2023. "Methodology for Environmental Risk Analysis Based on Intuitionistic Fuzzy Values," Risks, MDPI, vol. 11(5), pages 1-22, May.
    4. 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.
    5. England, Peter & Verrall, Richard, 1999. "Analytic and bootstrap estimates of prediction errors in claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 281-293, December.
    6. Haktanır, Elif & Kahraman, Cengiz, 2023. "Intuitionistic fuzzy risk adjusted discount rate and certainty equivalent methods for risky projects," International Journal of Production Economics, Elsevier, vol. 257(C).
    7. Lee, Haekwan & Tanaka, Hideo, 1999. "Upper and lower approximation models in interval regression using regression quantile techniques," European Journal of Operational Research, Elsevier, vol. 116(3), pages 653-666, August.
    8. 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.
    9. J. David Cummins & Richard Derrig, 1997. "Fuzzy Financial Pricing of Property-Liability Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 1(4), pages 21-40.
    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., 1977. "Separation of Inflation and other Effects from the Distribution of Non-Life Insurance Claim Delays," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 219-230, January.
    Full references (including those not matched with items on IDEAS)

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