Synthetic replication of American contingent claims when portfolios are constrained

This article studies the problem of synthetically replicating an American Contingent Claim using constrained portfolio policies. In particular, the asset mix of the replicating portfolio strategy must be maintained in a convex constraint set. Using the method of auxiliary markets of Cvitanic and Karatzas, the paper characterizes the unique replicating portfolio-consumption strategy and provides an upper bound for the fair market value of the claim. It also discusses the optimal time to exercise the claim.