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

Bouchard, Bruno; Possamaï, Dylan; Tan, Xiaolu (2016), A general Doob-Meyer-Mertens decomposition for g-supermartingale systems, Electronic Journal of Probability, 21, p. 21 p.. 10.1214/16-EJP4527

Type
Article accepté pour publication ou publié
External document link
http://dx.doi.org/10.1214/16-EJP4527
Date
2016
Journal name
Electronic Journal of Probability
Volume
21
Publisher
Electronic Journal of Probability and Electronic Communications in Probability
Pages
21 p.
Publication identifier
Metadata
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Author(s)
Bouchard, Bruno

Possamaï, Dylan

Tan, Xiaolu
Abstract (EN)
We provide a general Doob-Meyer decomposition for g-supermartingale systems, which does not require any right-continuity on the system, nor that the filtration is quasi left-continuous. In particular, it generalizes the Doob-Meyer decomposition of Mertens [36] for classical supermartingales, as well as Peng’s [41] 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 formulation for BSDEs with constraint on the gains-process, using very simple arguments.
Subjects / Keywords
Doob-Meyer decomposition; non-linear expectations; backward stochastic differential equations