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

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

2006-02-09

arxiv.org/abs/math/0602178v3

Mathematics

Probability

15 pages. Contains simplifications and amended notation

Scientific paper

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.

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