由布朗运动和列维过程联合驱动的一个有限期的线性二次最优随机控制问题（英文）  

A Finite Horizon Linear Quadratic Optimal Stochastic Control Problem Driven by Both Brownian Motion and Levy Processes

作　　者：胡世培 贺志民 HU Shipei;HE Zhimin(Jiyang College, Zhejiang A&F University, Zhuji, 311800, China)

机构地区：[1]浙江农林大学暨阳学院

出　　处：《应用概率统计》2019年第3期275-291,共17页Chinese Journal of Applied Probability and Statistics

摘　　要：我们研究了由布朗运动和列维过程联合驱动的线性二次最优随机控制问题.我们利用深刻的截口定理新的仿射随机微分方程存在逆过程.应用拟线性贝尔曼原理和单调迭代收敛方法,我们证明了倒向黎卡提微分方程解的存在性和唯一性.最后,我们证明了存在一个最优反馈控制且值函数由相应的倒向黎卡提微分方程和相应的伴随方程的初始值合成.We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and Levy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation.

关 键 词：线性二次最优随机控制问题 倒向黎卡提微分方程 列维过程 伴随方程 拟线性迭代方法 

分 类 号：O231.3[理学—运筹学与控制论] O211.63[理学—数学]