No arbitrage in discrete time under portfolio constraints

Laurence Carassus, Huye^n Pham, Nizar Touzi

Research output: Contribution to journalArticlepeer-review


In frictionless securities markets, the characterization of the no-arbitrage condition by the existence of equivalent martingale measures in discrete time is known as the fundamental theorem of asset pricing. In the presence of convex constraints on the trading strategies, we extend this theorem under a closedness condition and a nondegeneracy assumption. We then provide connections with the superreplication problem solved in Föllmer and Kramkov (1997).

Original languageEnglish (US)
Pages (from-to)315-329
Number of pages15
JournalMathematical Finance
Issue number3
StatePublished - Jul 2001


  • Arbitrage
  • Convex portfolio constraints
  • Fundamental theorem of asset pricing
  • Stochastic process
  • Superreplication cost

ASJC Scopus subject areas

  • Accounting
  • Social Sciences (miscellaneous)
  • Finance
  • Economics and Econometrics
  • Applied Mathematics


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