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Mean-variance hedging of unit linked life insurance contracts in a Levy model

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Added , Speaker Christian Dehm, Ulm Actuarial Day 2019, in 1ST ULM ACTUARIAL DAY | 5 MAR LIFE


Speaker: Christian Dehm, University of Ulm / ifa Ulm

“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.

Tags: Hedging

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