Francesco Ungolo and Patrick J. Laub
Abstract: The analysis of insurance and annuity products issued on multiple lives requires the use of statistical models which account for lifetime dependence. This work presents a Dirichlet Process Mixture-based approach which allows to model dependent lifetimes within a group, such as married couples, accounting for individual as well as group-specific covariates. The model is analysed in a fully Bayesian setting, and illustrated to jointly model the lifetime of male-female couples in a portfolio of joint and last survivor annuities of a Canadian life insurer. The inferential approach allows to account for right censoring and left truncation, which are common features of data in survival analysis. The model shows improved in-sample and out-of-sample performance compared to traditional approaches assuming independent lifetimes, and offers additional insights into the determinants of the dependence between lifetimes and their impact on joint and last survivor annuity prices.
Keywords: Dependent lifetimes, Survival Analysis, Dirichlet Process, Bayesian analysis, Life insurance, MCMC, Mixture models
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