Optimal Replication of Contingent Claims under Portfolio Constraints.

We determine the minimum cost of superreplicating a nonnegative contingent claim when there are convex constraints on portfolio weights. We 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 in an appropriate way relative to the original claim. The results hold for a variety of options, including some path-dependent options. Constraints on the gamma of the replicating portfolio, constraints on portfolio amounts, and constraints on the number of shares are also considered. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.