Frailty mixture model with application in insurance industry

Abstract

Heterogeneity in a population of assured lives in respect of mortality can be explained by differences among the individuals; some of these are observable, while others, for instance genetic factors having influence on survival are difficult to measure. This undermines usage of observable risk factors as the only rating factors for life insurance. This heterogeneity exposes insurers to adverse selection if only the healthiest lives purchase annuities, so standard annuities are priced with a mortality table that assumes above-average longevity. This makes standard annuities expensive for many individuals. To avoid biases in valuation a better understanding of heterogeneity in required. Frailty models are extensions of the Cox proportional hazards model which is popular in survival studies. The frailty approach is a statistical modeling method which aims to account for the heterogeneity caused by unmeasured covariates. It does so by adding random effects which act multiplicatively on the hazard. In this paper we consider the gamma, inverse gaussian and non-central gamma as frailty distributions with Weibull distribution as the baseline. The results shows that, the non-central gamma frailty model is appropriate for representation of the insurer’s liability when heterogeneity is present.