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No arbitrage in discrete time under portfolio constraints. (English) Zbl 1055.91018
Summary: 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 H. Föllmer and D. Kramkov [Probab. Theory Relat. Fields 109, No. 1, 1–25 (1997; Zbl 0882.60063)].

91B28 Finance etc. (MSC2000)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60G44 Martingales with continuous parameter
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