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BSDEs with mean reflection

Author

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  • Philippe Briand

    (LAMA)

  • Romuald Elie

    (LAMA)

  • Ying Hu

    (IRMAR)

Abstract

In this paper, we study a new type of BSDE, where the distribution of the Y-component of the solution is required to satisfy an additional constraint, written in terms of the expectation of a loss function. This constraint is imposed at any deterministic time t and is typically weaker than the classical pointwise one associated to reflected BSDEs. Focusing on solutions (Y, Z, K) with deterministic K, we obtain the well-posedness of such equation, in the presence of a natural Skorokhod type condition. Such condition indeed ensures the minimality of the enhanced solution, under an additional structural condition on the driver. Our results extend to the more general framework where the constraint is written in terms of a static risk measure on Y. In particular, we provide an application to the super hedging of claims under running risk management constraint.

Suggested Citation

  • Philippe Briand & Romuald Elie & Ying Hu, 2016. "BSDEs with mean reflection," Papers 1605.06301, arXiv.org.
    • Handle: RePEc:arx:papers:1605.06301
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    File URL: http://arxiv.org/pdf/1605.06301
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    Cited by:

    1. Roxana Dumitrescu & Romuald Elie & Wissal Sabbagh & Chao Zhou, 2017. "A new Mertens decomposition of $\mathscr{Y}^{g,\xi}$-submartingale systems. Application to BSDEs with weak constraints at stopping times," Papers 1708.05957, arXiv.org, revised May 2023.

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