BSDES WITH MEAN REFLECTION

• 成果类型: Article
• 署名作者: Briand, Philippe; Elie, Romuald; Hu, Ying
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Savoie Mont Blanc; CNRS - National Institute for Mathematical Sciences (INSMI); CNRS - Institute of Physics (INP); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Gustave-Eiffel; Inria; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1310
• 发表日期: 2018
• 页码: 482-510
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; Contingent claims; incomplete market

摘要

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.