Maximum Principle for Backward Stochastic Systems Associated with L′évy Processes Under Partial Information

摘要：

This paper studies an optimal control problem for a backward stochastic control systems associated with L′evy processes under partial information. More precisely, the controlled systems are described by backward stochastic differential equations driven by Teugels martingales and an independent multi-dimensional Brownian motion, where Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L′évy processes, and all admissible control processes are required to be adapted to a given subfiltration of the filtration generated by the underlying Teugels martingales and Brownian motion. For this type of partial information stochastic optimal control problem with convex control domain, we derive the necessary and sufficient conditions for the existence of the optimal control by means of convex analysis and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria (called backward linear-quadratic problem, or BLQ problem for short) under partial information is discussed and the unique optimal control is characterized explicitly by adjoint processes.

关键词： Stochastic control Stochastic maximum principle L′evy processes Teugels martingales Backward stochastic differential equations Partial information

作者: Meng Qingxin Zhang Fu Tang Maoning

作者单位: School of Mathematical Sciences, Fudan University, Shanghai 200433, China Department of Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China Department of Mathematics, Huzhou University, Huzhou 313000,China

会议类型: 国际会议

会议名称: The 31st Chinese Control Conference(第三十一届中国控制会议)

会议地点: 合肥

会议语种:英文

页码: 1628-1633

在线出版日期: 2012-07-01（万方平台首次上网日期，不代表论文的发表时间）