Frailty Models Applications In Pension Schemes

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 an individual's attitude towards health and/or all genetic factors having influence on survival are difficult to monitor and measure. This undermines usage of observable risk factors as the only rating factors for life insurance. Insurance companies have not taken proper care of unobservable risk factors possibly due to difficulties inherent in their modeling. 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. In many applications, the study population needs to be considered as a heterogeneous sample. Sometimes, due to lack of knowledge or for economical reasons, some covariates related to the event of interest are not measured. 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. This study carries out an extensive review of frailty models and is aimed at extending this work by considering other distributions that can be used in modeling. In particular, the non-central gamma distribution is proposed for frailty modeling.