BSDEs with mean reflection

Philippe Briand (), Romuald Elie and Ying Hu ()
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Philippe Briand: LAMA - Laboratoire de Mathématiques - USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc - CNRS - Centre National de la Recherche Scientifique
Romuald Elie: LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - BEZOUT - Fédération de Recherche Bézout - CNRS - Centre National de la Recherche Scientifique - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique
Ying Hu: IRMAR - Institut de Recherche Mathématique de Rennes - UR - Université de Rennes - INSA Rennes - Institut National des Sciences Appliquées - Rennes - INSA - Institut National des Sciences Appliquées - ENS Rennes - École normale supérieure - Rennes - UR2 - Université de Rennes 2 - CNRS - Centre National de la Recherche Scientifique - INSTITUT AGRO Agrocampus Ouest - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement

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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.

Keywords: Skorokhod type minimal condition; Super-hedging; risk management constraint; Backward stochastic differential equation; mean reflection (search for similar items in EconPapers)
Date: 2018
New Economics Papers: this item is included in nep-rmg
Note: View the original document on HAL open archive server: https://hal.science/hal-01318649v1
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Citations: View citations in EconPapers (11)

Published in The Annals of Applied Probability, 2018, 28 (1), pp.482-510. ⟨10.1214/17-AAP1310⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01318649

DOI: 10.1214/17-AAP1310

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