OPTIMAL DYNAMIC HEDGING IN INCOMPLETE FUTURES MARKETS

This article derives optimal hedging demands for futures contracts fro m an investor who cannot freely trade his portfolio of primitive asset s in the context of either a CARA or a logarithmic utility function. E xisting futures contracts are not numerous enough to complete the mark et. In addition, in the case of CARA, the nonnegativity constraint on wealth is binding, and the optimal hedging demands are not identical t o those that would be derived if the constraint were ignored. Fictitio usly completing the market, we can characterize the optimal hedging de mands for futures contracts. Closed-form solutions exist in the logari thmic case but not in the CARA case, since then a put (insurance) writ ten on his wealth is implicitly bought by the investor. Although solut ions are formally similar to those that obtain under complete markets, incompleteness leads in fact to second-best optima.