The Annals of Applied Probability

Arbitrage and duality in nondominated discrete-time models

Bruno Bouchard and Marcel Nutz

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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.

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

First available in Project Euclid: 19 February 2015

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

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


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.

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