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arXiv · 1505.00597

A general Doob-Meyer-Mertens decomposition for $g$-supermartingale systems

Bruno Bouchard·Dylan Possamaï·Xiaolu Tan
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Abstract

We provide a general Doob-Meyer decomposition for $g$-supermartingale systems, which does not require any right-continuity on the system. In particular, it generalizes the Doob-Meyer decomposition of Mertens (1972) for classical supermartingales, as well as Peng's (1999) version for right-continuous $g$-supermartingales. As examples of application, we prove an optional decomposition theorem for $g$-supermartingale systems, and also obtain a general version of the well-known dual formation for BSDEs with constraint on the gains-process, using very simple arguments.

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BibTeXRIS

Bruno Bouchard, Dylan Possamaï, Xiaolu Tan. 2015-07-23. A general Doob-Meyer-Mertens decomposition for $g$-supermartingale systems. https://arxiv.org/abs/1505.00597

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