No Arbitrage in Discrete Time Under Portfolio Constraints

Laurence Carassus, Huye^n Pham and Nizar Touzi

Mathematical Finance, 2001, vol. 11, issue 3, 315-329

Abstract: 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).

Date: 2001
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