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Nonparametric Estimation of Extreme Quantiles with an Application to Longevity Risk

Author

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  • Catalina Bolancé

    (Department Econometrics, Riskcenter-IREA, Universitat de Barcelona, 08007 Barcelona, Spain)

  • Montserrat Guillen

    (Department Econometrics, Riskcenter-IREA, Universitat de Barcelona, 08007 Barcelona, Spain)

Abstract

A new method to estimate longevity risk based on the kernel estimation of the extreme quantiles of truncated age-at-death distributions is proposed. Its theoretical properties are presented and a simulation study is reported. The flexible yet accurate estimation of extreme quantiles of age-at-death conditional on having survived a certain age is fundamental for evaluating the risk of lifetime insurance. Our proposal combines a parametric distributions with nonparametric sample information, leading to obtain an asymptotic unbiased estimator of extreme quantiles for alternative distributions with different right tail shape, i.e., heavy tail or exponential tail. A method for estimating the longevity risk of a continuous temporary annuity is also shown. We illustrate our proposal with an application to the official age-at-death statistics of the population in Spain.

Suggested Citation

  • Catalina Bolancé & Montserrat Guillen, 2021. "Nonparametric Estimation of Extreme Quantiles with an Application to Longevity Risk," Risks, MDPI, vol. 9(4), pages 1-23, April.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:4:p:77-:d:536622
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    References listed on IDEAS

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    Cited by:

    1. Mogens Steffensen, 2022. "Special Issue “Risks: Feature Papers 2021”," Risks, MDPI, vol. 10(3), pages 1-2, March.
    2. Catalina Bolancé & Carlos Alberto Acuña, 2021. "A New Kernel Estimator of Copulas Based on Beta Quantile Transformations," Mathematics, MDPI, vol. 9(10), pages 1-16, May.

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