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Modeling future lifetime as a fuzzy random variable

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  • Shapiro, Arnold F.

Abstract

A recent article by de Andrés-Sánchez and Puchades (2012) modeled life annuities as fuzzy random variables (FRVs). Their article was informative. However, it had the limitation that the FRV used to model the life annuity was not a granulated FRV. This followed because the authors assumed that the uncertainty insofar as mortality is entirely due to randomness and that the uncertainty with respect to interest rates is entirely due to fuzziness. The concern is that such a dichotomy may be problematic since, in actuality, the uncertainty of both the mortality parameter and the interest rate parameter can have both random and fuzzy features. The purpose of this article is to address the mortality portion of this dichotomy and, to this end, we model future lifetime as a FRV.

Suggested Citation

  • Shapiro, Arnold F., 2013. "Modeling future lifetime as a fuzzy random variable," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 864-870.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:864-870
    DOI: 10.1016/j.insmatheco.2013.10.007
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    References listed on IDEAS

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    1. Lemaire, Jean, 1990. "Fuzzy Insurance," ASTIN Bulletin, Cambridge University Press, vol. 20(1), pages 33-55, April.
    2. Virginia Young, 2004. "Optimal Investment Strategy to Minimize the Probability of Lifetime Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(4), pages 106-126.
    3. Suresh, K. R. & Mujumdar, P. P., 2004. "A fuzzy risk approach for performance evaluation of an irrigation reservoir system," Agricultural Water Management, Elsevier, vol. 69(3), pages 159-177, October.
    4. Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
    5. Nozer D. Singpurwalla & Jane M. Booker, 2004. "Membership Functions and Probability Measures of Fuzzy Sets," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 867-877, January.
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    Cited by:

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    3. Muhammad Shafiq & Muhammad Atif, 2017. "On the survival models for step-stress experiments based on fuzzy life time data," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(1), pages 79-91, January.
    4. Yao, Kai & Qin, Zhongfeng, 2015. "A modified insurance risk process with uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 227-233.
    5. Milevsky, Moshe A., 2020. "Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age?," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 147-161.
    6. Tazi, Nacef & Safaei, Fatemeh & Hnaien, Faicel, 2022. "Assessment of the levelized cost of energy using a stochastic model," Energy, Elsevier, vol. 238(PB).
    7. 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.
    8. Pablo J. Villacorta & Laura González-Vila Puchades & Jorge de Andrés-Sánchez, 2021. "Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance," Mathematics, MDPI, vol. 9(4), pages 1-23, February.

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