摘要：

The well-known Harrison-Plisse theorem claims that in the classical discrete time model of the financial market with finite Ω there is no arbitrage iff there exists an equivalent martingale measure. The famous Dalang-Morton-Willinger theorem extends this result for an arbitrary Ω. Kabanov and Strieker [KS01] generalized the Harrison-Pliska theorem for the case of the market with proportional transaction costs. Nevertheless the corresponding extension of the Kabanov and Strieker result to the case of non-finite Ω fails, the corresponding counter-example with 4 assets was constructed by Schachermayer [S04]. The main result of this paper is that in the special case of 2 assets the Kabanov and Strieker theorem can be extended for an arbitrary Ω. This is quite a surprising result since the corresponding cone of hedgeable claims (A{top}^){sub}T is not necessarily closed.

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