FBSDE with Poisson Process and its Application to Linear Quadratic Stochastic Optimal Control Problem with Random Jumps
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摘要: 给出一类布朗运动和泊松过程混合驱动的正倒向随机微分方程解的存在唯一性结果, 应用这一结果研究带有随机跳跃干扰的线性二次随机最优控制问题,并得到最优控制的显式形 式,可以证明最优控制是唯一的.然后,引入和研究一类推广的黎卡提方程系统,讨论该方程系统 的可解性并由该方程的解得到带有随机跳跃干扰的线性二次随机最优控制问题最优的线性反馈.Abstract: One kind of existence and uniqueness result of forward backward stochastic differential equations with Brownian motion and Poisson process is given. The result is applied to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem with random jumps. The optimal control can be proved to be unique. One kind of generalized Riccati equation system is introduced and its solvability is discussed. The linear feedback regulator for the optimal control problem with random jump is given by the solution of the generalized Riccati equation system.
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