Reflected BSDEs in non-convex domains

• 成果类型: Article
• 署名作者: Chassagneux, Jean-Francois; Nadtochiy, Sergey; Richou, Adrien
• 署名单位: Universite Paris Cite; Universite Paris Cite; Illinois Institute of Technology; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01125-0
• 发表日期: 2022
• 页码: 1237-1284
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; martingales; systems; uniqueness; MANIFOLDS; obstacle; limit

摘要

This paper establishes the well-posedness of reflected backward stochastic differential equations in non-convex domains that satisfy a weak version of the star-shaped property. The main results are established (i) in a Markovian framework with Holder-continuous generator and terminal condition and (ii) in a general setting under a smallness assumption on the input data. We also investigate the connections between this well-posedness result and the theory of martingales on manifolds, which, in particular, illustrates the sharpness of some of our assumptions.