Arbitrage and Duality in Nondominated Discrete-Time Models
Bouchard, Bruno; Nutz, Marcel (2015), Arbitrage and Duality in Nondominated Discrete-Time Models, The Annals of Applied Probability, 25, 2, p. 823-859. 10.1214/14-AAP1011
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1305.6008v3
Journal nameThe Annals of Applied Probability
Institute of Mathematical Statistics
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Abstract (EN)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.
Subjects / KeywordsKnightian uncertainty; Nondominated model; Superhedging; Optional decomposition; Fundamental Theorem of Asset Pricing; Martingale measure
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