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Article Dans Une Revue Electronic Journal of Probability Année : 2016

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

Résumé

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 for classical supermartingales, as well as Peng's 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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Dates et versions

hal-01148307 , version 1 (04-05-2015)
hal-01148307 , version 2 (23-07-2015)

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Bruno Bouchard, Dylan Possamaï, Xiaolu Tan. A general Doob-Meyer-Mertens decomposition for g-supermartingale systems. Electronic Journal of Probability, 2016, 21 (36), ⟨10.1214/16-EJP4527⟩. ⟨hal-01148307v2⟩
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