“Mean-variance hedging of unit linked life insurance contracts in a Levy model“ (joint work with Frank Bosserhoff and Mitja Stadje)
In this paper, we consider a mean variance optimization problem in a Levy market. To model the typical life insurance risks, we consider stochastic interest rate and mortality risk. Therefore, the insurance company is able to trade in a financial asset, a zero-coupon bond and a mortality bond driven by (possibly dependent) Levy processes. In order to find an optimal control, we reformulate the time inconsistent mean variance setting into a time consistent game theoretic framework to look for Nash subgame perfect equilibria (c.f. Bjoerk and Murgoci, 2010). Then the optimal trading strategies are characterized as solutions of PIDEs, the so-called extended HJB system. Finally, we are able to represent the optimal investment positions, the equilibrium value function and the expected terminal value in explicit form.