Application of the phase-type mortality law to life contingencies and risk management

The class of phase-type distributions has recently gained much popularity in insurance applications due to its mathematical tractability and denseness in the class of distributions defined on positive real line. In this paper, we show how to use the phase-type mortality law as an efficient risk management tool for various life insurance applications. In particular, pure premiums, benefit reserves, and risk-loaded premiums using CTE for standard life insurance products are shown to be available in analytic forms, leading to efficient computation and straightforward implementation. A way to explicitly determine provisions for adverse deviation for interest rate and mortality is also proposed. Furthermore, we show how the interest rate risk embedded in life insurance portfolios can be analyzed via interest rate sensitivity index and diversification index which are constructed based on the decomposition of portfolio variance. We also consider the applicability of phase-type mortality law under a few non-flat term structures of interest rate. Lastly, we explore how other properties of phase-type distributions may be applied to joint-life products as well as subgroup risk ordering and pricing within a given pool of insureds.