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A semiparametric method for assessing life expectancy evaluations. (English) Zbl 1479.91334

Summary: In the life settlements industry, life expectancy (LE) providers are firms that conduct health underwriting toward predicting the future mortality of an insured. Multiple stakeholders are interested in evaluating the quality of their assessments. There has been some recent interest in better alternatives to the traditional metric for this quality, the A/E ratio: the ratio of actual to expected number of deaths. One such alternative is the implied difference in life expectancies (IDLE) metric proposed by D. Bauer et al. [N. Am. Actuar. J. 22, No. 2, 198–209 (2018; Zbl 1393.91098)]. Its design largely retains the simplicity of the A/E ratio while being informative, unlike the A/E ratio, throughout the life of a policy block. Even though the IDLE is a significant improvement over the A/E ratio, it turns out that the IDLE is sensitive to departures from a key assumption, which motivates our development of a more robust metric. Our proposed methodology for evaluating the quality of the LE assessments involves using a survival regression model for estimating the mortality distribution of the insureds, with the average deviation of the life assessments from those derived using this model serving as a metric. In particular, we show that utilizing a Cox proportional hazards model with covariates derived from the LE assessments results in a robust yet well-performing alternative to both the A/E ratio and the IDLE.

MSC:

91G05 Actuarial mathematics
62P05 Applications of statistics to actuarial sciences and financial mathematics

Citations:

Zbl 1393.91098
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References:

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