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Generalization of Doob decomposition Theorem

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  • Nicholas Gonchar

Abstract

In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it an optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition onto the case of supermartingales relative to a convex set of equivalent measures.

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  • Nicholas Gonchar, 2016. "Generalization of Doob decomposition Theorem," Papers 1601.03574, arXiv.org.
    • Handle: RePEc:arx:papers:1601.03574
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    1. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
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