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No-arbitrage and closure results for trading cones with transaction costs

Research paper by Saul Jacka, Abdelkarem Berkaoui, Jon Warren

Indexed on: 24 Apr '08Published on: 24 Apr '08Published in: Mathematics - Probability



Abstract

The paper considers trading with proportional transaction costs. We give a necessary and sufficient condition for A, the cone of claims attainable from zero endowment, to be closed, and show, in general, how to represent its closure in such a way that it is the cone of claims attainable for zero endowment, for a different set of trading prices. The new representation obeys the Fundamental Theorem of Asset Pricing. We then show how to represent claims and in a final section show how any such setup corresponds to a coherent risk measure.