The Mean-Variance Hedging in a Bond Market with Jumps

Abstract

We construct a market of bonds with jumps driven by a general marked point process as well as by a ℝ n -valued Wiener process based on Björk et al. [6], in which there exists at least one equivalent martingale measure Q 0. Then we consider the mean-variance hedging of a contingent claim H ∈ L 2(ℱ T 0 ) based on the self-financing portfolio based on the given maturities T 1,…, T n with T 0 < T 1 < … <T n ≤ T*. We introduce the concept of variance-optimal martingale (VOM) and describe the VOM by a backward semimartingale equation (BSE). By making use of the concept of ℰ*-martingales introduced by Choulli et al. [8], we obtain another BSE which has a unique solution. We derive an explicit solution of the optimal strategy and the optimal cost of the mean-variance hedging by the solutions of these two BSEs.