OPTIMAL REPLICATION OF CONTINGENT CLAIMS UNDER PORTFOLIO CONSTRAINTS

We determine the minimum cost of super-replicating a nonnegative conti ngent claim when there are convex constraints on portfolio weights. Ne show that the optimal cost with constraints is equal to the price of a related claim without constraints. The related claim is a dominating claim, that is, a claim whose payoffs are increased ire an appropriat e way relative to the original claim. The results hold for a variety o f options, including some path-dependent options. Constraints on the g amma of the replicating portfolio, constraints on portfolio amounts, a nd constraints on the number of shares are also considered.