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arXiv · 1811.11621

Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs

Christoph Kühn·Alexander Molitor
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Abstract

In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Kabanov, Rásonyi, and Stricker (2002). The prospective strict no-arbitrage condition is slightly weaker than robust no-arbitrage, and it implies that the set of portfolios attainable from zero initial endowment is closed in probability. A weak version of prospective strict no-arbitrage turns out to be equivalent to the existence of a consistent price system. In contrast to the fundamental theorem of asset pricing of Schachermayer (2004), the consistent frictionless prices may lie on the boundary of the bid-ask spread. On the technical level, a crucial difference to Schachermayer (2004) and Kabanov-Rásonyi-Stricker (2003) is that we prove closedness without having at hand that the null-strategies form a linear space.

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Christoph Kühn, Alexander Molitor. 2019-04-30. Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs. https://doi.org/10.1007/s00780-019-00403-5

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