No arbitrage conditions and liquidity

Fabian Astic, Nizar Touzi

Research output: Contribution to journalArticlepeer-review


We extend the fundamental theorem of asset pricing to the case of markets with liquidity risk. Our results generalize, when the probability space is finite, those obtained by Kabanov et al. [Kabanov, Y., Stricker, C., 2001. The Harrison-Pliska arbitrage pricing theorem under transaction costs. Journal of Mathematical Economics 35, 185-196; Kabanov, Y., Rásonyi, M., Stricker, C., 2002. No-arbitrage criteria for financial markets with efficient friction. Finance and Stochastics 6, 371-382; Kabanov, Y., Rásonyi, M., Stricker, C., 2003. On the closedness of sums of convex cones in L0 and the robust no-arbitrage property. Finance and Stochastics] and by Schachermayer [Schachermayer, W., 2004. The fundamental theorem of asset pricing under poportional transaction costs in finite discrete time. Mathematical Finance 14 (1), 19-48] for markets with proportional transaction costs. More precisely, we restate the notions of consistent and strictly consistent price systems and prove their equivalence to corresponding no arbitrage conditions. We express these results in an analytical form in terms of the subdifferential of the so-called liquidation function. We conclude the paper with a hedging theorem.

Original languageEnglish (US)
Pages (from-to)692-708
Number of pages17
JournalJournal of Mathematical Economics
Issue number6
StatePublished - Aug 2007


  • Arbitrage theory
  • Hedging
  • Liquidity
  • Separation theorems
  • Transaction costs

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics


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