Infinite-Horizon Optimal Hedging Under Cone Constraints

Abstract

We address the issue of hedging in infinite horizon markets with a type of constraints that the set of feasible portfolio holdings forms a convex cone. We show that the minimum cost of hedging a liability stream is equal to its largest present value with respect to admissible stochastic discount factors, thus can be determined without finding an optimal hedging strategy. We solve for an optimal hedging strategy by solving a sequence of independent one-period hedging problems. We apply the results to a variety of trading restrictions and also show how the admissible stochastic discount factors can be characterized.