Synthetic replication of American contingent claims when portfolios are constrained

This article studies the problem of synthetically replicating an American Contingent Claim (ACC) 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 (1992), we characterize the unique replicating portfolio—consumption strategy and provide an upper bound for the fair market value of the claim. We also discuss the optimal time to exercise the claim.