MEAN-FIELD REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

• 成果类型: Article
• 署名作者: Djehiche, Boualem; Elie, Romuald; Hamadene, Said
• 署名单位: Royal Institute of Technology; Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Le Mans Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1657
• 发表日期: 2023
• 页码: 2493-2518
• 关键词: constraints; BSDEs; games

摘要

In this paper, we study a class of reflected backward stochastic differen-tial equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the Y-component of the solution enters in both the driver and the lower obstacle. We consider in details the case where the lower obstacle is a deterministic function of (Y, E[Y]) and discuss the more general dependence on the distribution of Y. Under mild Lipschitz and in-tegrability conditions on the coefficients, we obtain the well-posedness of such a class of equations. Under further monotonicity conditions, we show convergence of the standard penalization scheme to the solution of the equa-tion, which hence satisfies a minimality property. This class of equations is motivated by applications in pricing life insurance contracts with surrender options.