Positive Stable Frailty Approach in the Construction of Dependence Life-Tables

Abstract

Dependence may arise in insurance when the insureds are clustered into groups e.g. joint-life annuities. This dependence may be produced by sharing a common risk acting on mortality of members of the group. Various dependence models have been considered in literature ; however, the focus has been on either the lower-tail dependence alone or upper-tail dependence alone. This article implements the frailty dependence approach to life insurance problems where most applications have been within medical setting. Our strategy is to use the conditional independence assumption given an observed association measure in a positive stable frailty approach to account for both lower and upper-tail dependence. The model is calibrated on the association of Kenyan insurers 2010 male and female published rates. The positive stable model is then proposed to construct dependence life-tables and generate life annuity payment streams in the competitive Kenyan market.