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**1 - 2**of**2**### ON THE DENSITY OF PROPERLY MAXIMAL CLAIMS IN FINANCIAL MARKETS WITH TRANSACTION COSTS.

, 2008

"... Abstract. We consider trading in a financial market with proportional transaction costs. We prove that although, in distinction to the frictionless case, the maximal claims are not necessarily priced by any consistent price process (the equivalent of an EMM), the properly maximal claims are, and the ..."

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Abstract. We consider trading in a financial market with proportional transaction costs. We prove that although, in distinction to the frictionless case, the maximal claims are not necessarily priced by any consistent price process (the equivalent of an EMM), the properly maximal claims are, and they are dense in the set of maximal claims (with the topology of convergence in probability).

### ON REPRESENTING CLAIMS FOR COHERENT RISK MEASURES

"... Abstract. We consider the problem of representing claims for coherent risk measures. For this purpose we introduce the concept of (weak and strong) time-consistency with respect to a portfolio of assets, generalizing the one defined in Delbaen [7]. In a similar way we extend the notion of m-stabilit ..."

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Abstract. We consider the problem of representing claims for coherent risk measures. For this purpose we introduce the concept of (weak and strong) time-consistency with respect to a portfolio of assets, generalizing the one defined in Delbaen [7]. In a similar way we extend the notion of m-stability, by introducing weak and strong versions. We then prove that the two concepts of m- stability and time-consistency are still equivalent, thus giving necessary and sufficient conditions for a coherent risk measure to be represented by a market with proportional transaction costs. We go on to deduce that, under a separability assumption, any coherent risk measure is strongly time-consistent with respect to a suitably chosen countable portfolio, and show the converse: that any market with proportional transaction costs is equivalent to a market priced by a coherent risk measure, essentially establishing the equivalence of the two concepts.