No arbitrage conditions and liquidity
Astic, Fabian; Touzi, Nizar (2007), No arbitrage conditions and liquidity, Journal of Mathematical Economics, 43, 6, p. 692-708. http://dx.doi.org/10.1016/j.jmateco.2006.10.005
TypeArticle accepté pour publication ou publié
Journal nameJournal of Mathematical Economics
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Abstract (EN)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 L0L0 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.
Subjects / KeywordsArbitrage theory; Liquidity; Transaction costs; Hedging; Separation theorems
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