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

Christoph Kühn () and Alexander Molitor ()
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Christoph Kühn: Goethe-Universität Frankfurt
Alexander Molitor: Goethe-Universität Frankfurt

Finance and Stochastics, 2019, vol. 23, issue 4, No 9, 1049-1077

Abstract: Abstract In discrete-time markets with proportional transaction costs, Schachermayer (Math. Financ. 14:19–48, 2004) showed 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 et al. (Finance Stoch. 6:371–382, 2002). The prospective strict no-arbitrage condition is slightly weaker than the robust no-arbitrage condition, 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 (Math. Financ. 14:19–48, 2004), the consistent frictionless prices may lie on the boundary of the bid–ask spread. On the technical level, a crucial difference to Schachermayer (Math. Financ. 14:19–48, 2004) and Kabanov et al. (Finance Stoch. 7:403–411, 2003) is that we prove closedness without having at hand that the null-strategies form a linear space.

Keywords: Proportional transaction costs; Arbitrage; Fundamental theorem of asset pricing; 60G42; 91G10 (search for similar items in EconPapers)
JEL-codes: G11 G12 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00780-019-00403-5

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