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NoArbitrage Pricing for DividendPaying Securities in DiscreteTime Markets with Transaction Costs
"... We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discretetime markets with dividendpaying securities. Specifically, we show that the noarbitrage condition under the efficient friction assumption is equivalent to the existence of a riskneutral measure. ..."
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We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discretetime markets with dividendpaying securities. Specifically, we show that the noarbitrage condition under the efficient friction assumption is equivalent to the existence of a riskneutral measure. We derive dual representations for the superhedging ask and subhedging bid price processes of a contingent claim. Our results are illustrated with a vanilla credit default swap contract.
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) timeconsistency with respect to a portfolio of assets, generalizing the one defined in Delbaen [7]. In a similar way we extend the notion of mstabilit ..."
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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) timeconsistency with respect to a portfolio of assets, generalizing the one defined in Delbaen [7]. In a similar way we extend the notion of mstability, by introducing weak and strong versions. We then prove that the two concepts of m stability and timeconsistency 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 timeconsistent 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.
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).