No-arbitrage with multiple-priors in discrete time

Romain Blanchard and Laurence Carassus

Stochastic Processes and their Applications, 2020, vol. 130, issue 11, 6657-6688

Abstract: In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. We show that it is equivalent to the existence of a subclass of priors having the same polar sets as the initial class and such that the uni-prior no-arbitrage holds true for all priors in this subset. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and allowing the proof of important results in mathematical finance. We also revisit the geometric and quantitative no-arbitrage conditions and explicit two important examples where all these concepts are illustrated.

Keywords: No-arbitrage; Knightian uncertainty; Multiple-priors; Non-dominated model (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.spa.2020.06.006

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