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.
Highlights
Introduction and MotivationWhen annuity payments are concerned, the calculation of expected present values (EPVs), needed in pricing and reserving, requires an appropriate mortality model in order to avoid biased valuations [1] [2] [3]
We present below four examples with specific baseline distributions to find the frailty dependence hazard functions with explicit expressions
On the basis of Bayesian the Weibull distribution is chosen since the deviance information criteria (DIC), Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are smallest compared to the other distributions
Summary
Introduction and MotivationWhen annuity payments are concerned, the calculation of expected present values (EPVs), needed in pricing and reserving, requires an appropriate mortality model in order to avoid biased valuations [1] [2] [3]. Frailty models are used in life insurance to represent heterogeneity in a population due to unreported risk factors [4] [5]. There has been a growing literature on dependence mortality modeling in life insurance in recent years Frailty dependence modeling [9] [10] [11] [12] is an approach that accounts for dependence in event times of related individuals. Clustered survival times are assumed to be conditional independent with respect to the shared risk. Our strategy is to use the conditional independence assumption to account for lower and upper-tail dependence for a given association measure. This article implements the dependence frailty approach in insurance risk management setting
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