Relative Hedging of Systematic Mortality Risk

Abstract

We study indifference valuation mechanisms for mortality contingent claims under stochastic mortality age structures. Our focus is on capturing the internal cross-hedge between components of an insurer’s portfolio, especially between life annuities and life insurance. We carry out an exhaustive analysis of the dynamic exponential premium principle, which is the representative nonlinear valuation rule in our framework. Using this valuation rule we derive formulas for optimal quantity of contracts to sell. Our results are further enhanced by asymptotic expansions that show the relative effects of model parameters. We also compare the exponential premium principle to other valuation rules. Furthermore, we provide numerical examples to illustrate our approach.