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. 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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2015
- DOI:
- 10.48550/arXiv.1505.00597
- arXiv:
- arXiv:1505.00597
- Bibcode:
- 2015arXiv150500597B
- Keywords:
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- Mathematics - Probability;
- Mathematics - Optimization and Control;
- Quantitative Finance - Mathematical Finance;
- 60H99
- E-Print:
- 28 pages