## Electronic Journal of Probability

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

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 36, 21 pp.

Dates
Accepted: 25 April 2016
First available in Project Euclid: 2 May 2016

https://projecteuclid.org/euclid.ejp/1462192627

Digital Object Identifier
doi:10.1214/16-EJP4527

Mathematical Reviews number (MathSciNet)
MR3508683

Zentralblatt MATH identifier
1343.60050

Subjects
Primary: 60H99: None of the above, but in this section

#### Citation

Bouchard, Bruno; Possamaï, Dylan; Tan, Xiaolu. A general Doob-Meyer-Mertens decomposition for g-supermartingale systems. Electron. J. Probab. 21 (2016), paper no. 36, 21 pp. doi:10.1214/16-EJP4527. https://projecteuclid.org/euclid.ejp/1462192627

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