Summary 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 Stricker [KS01] generalized the Harrison–Pliska theorem for the case of the market with proportional transaction costs. Nevertheless the corresponding extension of the Kabanov and Stricker 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 Stricker theorem can be extended for an arbitrary Ω. This is quite a surprising result since the corresponding cone of hedgeable claims ÂT is not necessarily closed.

Coherent risk measures, Convex risk measures, Dilatation monotonicity, Factor monotonicity, Fatou property, Law invariance, Second-order stochastic dominance, G32, 91B16, 91B30,

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SUMMARY The purpose of our paper is to link some results on the Choquet integrals with the theory of coherent risk measures. Using this link we establish some properties of dilatation monotone and comonotonic coherent measures of risk. In particular it is shown that on an atomless probability space dilatation monotone and comonotonic additive coherent risk measures have to be law invariant.

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