Abstract
We study the problem of determining the minimum cost of super-replicating a non-negative contingent claim when there are convex constraints on the portfolio weights. It is shown that the optimal cost with constraints is equal to the price of a related claim without constraints. The related claim is a dominating claim, i.e., a claim whose payoffs are increased in an appropriate way relative to the original claim. The results hold for a wide variety of options, including standard European and American calls and puts, multi-asset options, and some path-dependent options. We also provide somewhat similar analysis when there are constraints on the gamma of the replicating portfolio.
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