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Erscheinungsjahr: 
2021
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 9 [Issue:] 4 [Article No.:] 77 [Publisher:] MDPI [Place:] Basel [Year:] 2021 [Pages:] 1-23
Verlag: 
MDPI, Basel
Zusammenfassung: 
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.
Schlagwörter: 
extreme quantile
extreme value distribution
kernel estimation
lifetime annuity
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