Sampled control for mean-variance hedging in a jump diffusion financial market

Abstract

In this paper we consider the mean-variance hedging problem of a jump diffusion continuous state space financial model with the re-balancing strategies for the hedging portfolio taken at discrete times, a situation that more closely reflects real market conditions. A direct expression based on some change of measures, not depending on any recursions, is derived for the optimal self-financing mean-variance hedging strategy problem as well as for the 'fair hedging price', considering any given payoff. For the case of a European call option these expressions can be evaluated in a closed form.