MEAN VARIANCE HEDGING IN A GENERAL JUMP MARKET

Abstract

We consider a financial market in which the discounted price process S is an ℝd-valued semimartingale with bounded jumps, and the variance-optimal martingale measure (VOMM) Q opt is only known to be a signed measure. We give a backward semimartingale equation (BSE) and show that the density process Z opt of Q opt with respect to P is a possibly non-positive stochastic exponential if and only if this BSE has a solution. For a general contingent claim H, we consider the following generalized version of the classical mean-variance hedging problem [Formula: see text] where [Formula: see text]. We represent the optimal strategy and the optimal cost of the mean-variance hedging by means of another backward martingale equation (BME) and an appropriate predictable process δ both with a straightforward intuitive interpretation.