Reflected solutions of backward SDE's, and related obstacle problems for PDE's

• 成果类型: Article
• 署名作者: El Karoui, N; Kapoudjian, C; Pardoux, E; Peng, S; Quenez, MC
• 署名单位: Sorbonne Universite; Aix-Marseille Universite; Ecole Normale Superieure de Lyon (ENS de LYON); Shandong University; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1997
• 页码: 702-737
• 关键词: equations

摘要

We study reflected solutions of one-dimensional backward stochastic differential equations. The reflection keeps the solution above a given stochastic process. We prove uniqueness and existence both by a fixed point argument and by approximation via penalization. We show that when the coefficient has a special form, then the solution of our problem is the value function of a mixed optimal stopping-optimal stochastic control problem. We finally show that, when put in a Markovian framework, the solution of our reflected BSDE provides a probabilistic formula for the unique viscosity solution of an obstacle problem for a parabolic partial differential equation.