No arbitrage in discrete time under portfolio constraints

Laurence Carassus; Huye^n Pham; Nizar Touzi

doi:10.1111/1467-9965.00117

No arbitrage in discrete time under portfolio constraints

Laurence Carassus, Huye^n Pham, Nizar Touzi

Finance and Risk Engineering

Research output: Contribution to journal › Article › peer-review

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).

Original language	English (US)
Pages (from-to)	315-329
Number of pages	15
Journal	Mathematical Finance
Volume	11
Issue number	3
DOIs	https://doi.org/10.1111/1467-9965.00117
State	Published - Jul 2001

Keywords

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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10.1111/1467-9965.00117

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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 F{\"o}llmer and Kramkov (1997).",

keywords = "Arbitrage, Convex portfolio constraints, Fundamental theorem of asset pricing, Stochastic process, Superreplication cost",

author = "Laurence Carassus and Huye^n Pham and Nizar Touzi",

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AB - 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).

KW - Arbitrage

KW - Convex portfolio constraints

KW - Fundamental theorem of asset pricing

KW - Stochastic process

KW - Superreplication cost

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No arbitrage in discrete time under portfolio constraints

Abstract

Keywords

ASJC Scopus subject areas

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