BACKWARD SDES WITH CONSTRAINED JUMPS AND QUASI-VARIATIONAL INEQUALITIES

• 成果类型: Article
• 署名作者: Kharroubi, Idris; Ma, Jin; Pham, Huyen; Zhang, Jianfeng
• 署名单位: Institut Polytechnique de Paris; ENSAE Paris; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Southern California
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP496
• 发表日期: 2010
• 页码: 794-840
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; Contingent claims

摘要

We consider a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution for the BSDEs by using a penalization approach. Moreover, we show that under mild conditions the minimal solutions to these constrained BSDEs can be characterized as the unique viscosity solution of quasi-variational inequalities (QVIs), which leads to a probabilistic representation for solutions to QVIs. Such a representation in particular gives a new stochastic formula for value functions of a class of impulse control problems. As a direct consequence, this suggests a numerical scheme for the solution of such QVIs via the simulation of the penalized BSDEs.