We determine the minimum cost of super-replicating 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 the portfolio amounts, and constraints on the number of shares are also considered.
Broadie, Mark, J. Cvitanic, and M. Soner. "Optimal Replication of Contingent Claims Under Portfolio Constraints." Review of Financial Studies 11, no. 1 (1998): 59-79.
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