【摘要】 研究了由Teugels鞅和与之独立的多维Brown运动共同驱动的正倒向随机控制系统的最优控制问题.这里Teugels鞅是一列与Levy过程相关的两两强正交的正态鞅(见Nualart,Schoutens在2000年的结果).在允许控制值域为一非空凸闭集假设下,采用凸变分法和对偶技术获得了最优控制存在所满足的充分和必要条件.作为应用,系统研究了线性正倒向随机系统的二次最优控制问题(简记为FBLQ问题),通过相应的随机哈密顿系统对最优控制进行了对偶刻画.这里的随机哈密顿系统是由Teugels鞅和多维Brown运动共同驱动的线性正倒向随机微分方程,其由状态方程、伴随方程和最优控制的对偶表示共同来构成.更多还原

【Abstract】 The paper is concerned with a stochastic optimal control problem,where the controlled systems are forward-backward stochastic differential equations(or FBSDEs for short) driven by Teugels martingales and an independent multi-dimensional Brownian motion.Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with Levy processes(see the results of Nualart and Schoutens in 2000).We derive the necessary and sufficient conditions for the existence of the optimal control in a stochastic maximum principle by means of convex variation methods and duality techniques when the control domain is convex.As an application,the optimal control problem of linear forward-backward stochastic systems with a quadratic cost criteria(called forward-backward linear-quadratic problem,or FBLQ problem for short) is discussed and characterized by stochastic Hamilton system.Here,the stochastic Hamilton system is a linear forward-backward stochastic differential equation with double dimensions driven by Teugels martingales and an independent multi-dimensional Brownian motion,consisting of state equation,adjoint equation and dual presentation of the optimal control.更多还原