Stochastic Mortality: Experience-Based Modeling and Application Issues Consistent with Solvency 2

Abstract

This paper is motivated by the need to have appropriate tools for the valuation of mortality risks when carrying out an internal assessment of the insurance business, such as a portfolio valuation or a solvency investigation based on internal models. The case of life annuities is in particular addressed, due to the importance of mortality on the cost of living benefits for the elderly. Our aim is to describe a stochastic mortality model calibrated on the best-estimate life table available to the insurer and to the mortality experienced in the insurer's portfolio. As we address life annuities, uncertainty of future mortality improvements, i.e. the aggregate mortality risk, needs in particular to be accounted for. Following Olivieri and Pitacco (2009), we extend some classical results about the modeling of the number of deaths joint to the modeling of parameter uncertainty. We explore the features of two alternative approaches: a Beta-Binomial and a Poisson-Gamma setting; we then focus on the latter only. Thanks to a Bayesian inferential procedure, the parameters, initially assigned referring to the best-estimate life table, are updated according to the mortality experienced in the portfolio. Extending a traditional tool-kit, the framework we define is in particular suitable for practical work. Due to calibration, clearly the scope of the model is within internal assessments. To provide an example of application of the model, we perform a capital assessment. Solvency rules which could be adopted as an alternative to a standard, regulatory requirement are tested. The Solvency 2 requirement for longevity risk is referred to for the design of an internal rule which could get validation for replacing the standard one.

Keywords: Life annuities, Random fluctuations, Systematic deviations, Process risk, Longevity risk, Solvency

JEL Classification: C00, G22