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

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  • Bruno Bouchard
  • Dylan Possamai
  • Xiaolu Tan

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.

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  • Bruno Bouchard & Dylan Possamai & Xiaolu Tan, 2015. "A general Doob-Meyer-Mertens decomposition for $g$-supermartingale systems," Papers 1505.00597, arXiv.org, revised Jul 2015.
    • Handle: RePEc:arx:papers:1505.00597
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    References listed on IDEAS

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    1. Chen, Zengjing & Peng, Shige, 2000. "A general downcrossing inequality for g-martingales," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 169-175, January.
    2. Anis Matoussi & Lambert Piozin & Dylan Possamai, 2012. "Second-order BSDEs with general reflection and game options under uncertainty," Papers 1212.0476, arXiv.org, revised Jan 2014.
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    Cited by:

    1. Dylan Possamai & Xiaolu Tan & Chao Zhou, 2015. "Stochastic control for a class of nonlinear kernels and applications," Papers 1510.08439, arXiv.org, revised Jul 2017.

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