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Optimality of the replicating strategy for American options. (English) Zbl 1050.91514
Summary: The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox-Ross-Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an optimal replicating strategy that is not optimal in the global sense.

MSC:
91B28 Finance etc. (MSC2000)
91B24 Microeconomic theory (price theory and economic markets)
93E20 Optimal stochastic control
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