The Annals of Applied Probability

Arbitrage and duality in nondominated discrete-time models

Bruno Bouchard and Marcel Nutz

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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.

Article information

Source
Ann. Appl. Probab. Volume 25, Number 2 (2015), 823-859.

Dates
First available in Project Euclid: 19 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1424355131

Digital Object Identifier
doi:10.1214/14-AAP1011

Mathematical Reviews number (MathSciNet)
MR3313756

Zentralblatt MATH identifier
1322.60045

Subjects
Primary: 60G42: Martingales with discrete parameter 91B28 93E20: Optimal stochastic control 49L20: Dynamic programming method

Keywords
Knightian uncertainty nondominated model Fundamental Theorem of Asset Pricing martingale measure superhedging optional decomposition

Citation

Bouchard, Bruno; Nutz, Marcel. Arbitrage and duality in nondominated discrete-time models. Ann. Appl. Probab. 25 (2015), no. 2, 823--859. doi:10.1214/14-AAP1011. https://projecteuclid.org/euclid.aoap/1424355131.


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