Optimal replication of contingent claims under portfolio constraints |
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Authors: | Broadie M; Cvitanic J; Soner HM |
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Institution: | 1 Department of Statistics, Columbia University, 2990 Broadway, Mail Code 4403, New York, NY 10027, USA
2 Carnegie Mellon University and Bogazici University, USA
z Corresponding author e-mail: cj@stat.columbia.edu |
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Abstract: | We determine the minimum cost of super-replicating a nonnegativecontingent claim when there are convex constraints on portfolioweights. We show that the optimal cost with constraints is equalto the price of a related claim without constraints. The relatedclaim is a dominating claim, that is, a claim whose payoffsare increased in an appropriate way relative to the originalclaim. The results hold for a variety of options, includingsome path-dependent options. Constraints on the gamma of thereplicating portfolio, constraints on the portfolio amounts,and constraints on the number of shares are also considered. |
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