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A closed-form solution to the problem of super-replication under transaction costs. (English) Zbl 0924.90010
The authors investigate the problem of finding the minimal price needed to dominate European-type contingent claims under proportional transaction costs in a Markovian continuous-time model. Using a representation of the minimal super-replication price as a supremum for the expectations of the claim under the equivalent probability measure under which the appropriately discounted wealth process is a supermartingale the authors show that the least expensive dominating strategy for general path-independent contingent claims is equal to the least expensive buy-and-hold strategy. The viscosity solutions approach to that stochastic control problem is used.

MSC:
91B28 Finance etc. (MSC2000)
93E20 Optimal stochastic control
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