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

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Date
2016
Link to item file
http://dx.doi.org/10.1214/16-EJP4527
Dewey
Probabilités et mathématiques appliquées
Sujet
Doob-Meyer decomposition; non-linear expectations; backward stochastic differential equations
Journal issue
Electronic Journal of Probability
Volume
21
Publication date
2016
Article pages
21 p.
Publisher
Electronic Journal of Probability and Electronic Communications in Probability
DOI
http://dx.doi.org/10.1214/16-EJP4527
URI
https://basepub.dauphine.fr/handle/123456789/16168
Collections
  • CEREMADE : Publications
Metadata
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Author
Bouchard, Bruno
Possamaï, Dylan
Tan, Xiaolu
Type
Article accepté pour publication ou publié
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.

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