Indifference pricing of a life insurance portfolio with systematic mortality risk in a market with an asset driven by a Lévy process

Abstract

In this paper, we investigate the problem of pricing and hedging of life insurance liabilities. We consider a financial market consisting of a risk-free asset with a constant rate of return, and a risky asset whose price is driven by a Lévy process. We take into account a systematic mortality risk and model mortality intensity as a diffusion process. The principle of equivalent utility is chosen as the valuation rule. In order to solve our optimization problems, we apply techniques from the stochastic control theory. An exponential utility is considered in detail. We arrive at three pricing equations and investigate some properties of the premiums. An estimate of the finite-time ruin probability is derived. Indifference pricing with respect to a quadratic loss function is also briefly discussed.