Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts

Abstract

In life insurance, actuaries have traditionally calculated premiums and reserves using a deterministic mortality intensity, which is a function of the age of the insured only. Here, we model the mortality intensity as a stochastic process. This allows us to capture two important features of the mortality intensity: Time dependency and uncertainty of the future development. The advantage of introducing a stochastic mortality intensity is twofold. Firstly, it gives more realistic premiums and reserves, and secondly, it quantifies the risk of the insurance companies associated with the underlying mortality intensity. Having introduced a stochastic mortality intensity, we study possible ways of transferring the systematic mortality risk to other parties. One possibility is to introduce mortality-linked insurance contracts. Here the premiums and/or benefits are linked to the development of the mortality intensity, thereby transferring the systematic mortality risk to the insured. Alternatively, the insurance company can transfer some or all of the systematic mortality risk to agents in the financial market by trading derivatives depending on the mortality intensity.