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April 2015 Arbitrage and duality in nondominated discrete-time models
Bruno Bouchard, Marcel Nutz
Ann. Appl. Probab. 25(2): 823-859 (April 2015). DOI: 10.1214/14-AAP1011

Abstract

We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of martingale measures. In the arbitrage-free case, we show that optimal superhedging strategies exist for general contingent claims, and that the minimal superhedging price is given by the supremum over the martingale measures. Moreover, we obtain a nondominated version of the Optional Decomposition Theorem.

Citation

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Bruno Bouchard. Marcel Nutz. "Arbitrage and duality in nondominated discrete-time models." Ann. Appl. Probab. 25 (2) 823 - 859, April 2015. https://doi.org/10.1214/14-AAP1011

Information

Published: April 2015
First available in Project Euclid: 19 February 2015

zbMATH: 1322.60045
MathSciNet: MR3313756
Digital Object Identifier: 10.1214/14-AAP1011

Subjects:
Primary: 49L20, 60G42, 91B28, 93E20

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 2 • April 2015
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