On a class of optimization problems emerging when hedging with short term futures contracts

This paper generalizes earlier work by G. Larcher and the author about hedging with short-term futures contracts, a problem which was considered in connection with the debacle of the German company Metallgesellschaft. While the original problem corresponded to the simplest possible model for the price process, i.e. Brownian motion, we give here solutions to more general models, i.e. a mean reverting model (Ornstein-Uhlenbeck process) and geometric Brownian motion. Furthermore we allow for interest rates greater than 0.