Optimal Replication of Contingent Claims Under Portfolio Constraints
Coauthor(s): J. Cvitanic, M. Soner.
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.
Source: Review of Financial Studies
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.