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February 2018 BSDEs with mean reflection
Philippe Briand, Romuald Elie, Ying Hu
Ann. Appl. Probab. 28(1): 482-510 (February 2018). DOI: 10.1214/17-AAP1310

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.

Citation

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Philippe Briand. Romuald Elie. Ying Hu. "BSDEs with mean reflection." Ann. Appl. Probab. 28 (1) 482 - 510, February 2018. https://doi.org/10.1214/17-AAP1310

Information

Received: 1 May 2016; Revised: 1 January 2017; Published: February 2018
First available in Project Euclid: 3 March 2018

zbMATH: 06873689
MathSciNet: MR3770882
Digital Object Identifier: 10.1214/17-AAP1310

Subjects:
Primary: 60H10, 91G10

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 1 • February 2018
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