Indefinite stochastic linear-quadratic optimal control problems with random jumps and related stochastic Riccati equations

被引：0

作者：

Na Li ^{[1
]}

Zhen Wu ^{[2
]}

Zhiyong Yu ^{[2
]}

机构：

[1] School of Statistics, Shandong University of Finance and Economics

[2] School of Mathematics, Shandong University

来源：

Science China(Mathematics) | 2018年 / 61卷 / 03期

基金：

中国国家自然科学基金;

关键词：

stochastic linear-quadratic problem; Hamiltonian system; Riccati equation; Poisson process; indefinite case;

D O I：

暂无

中图分类号：

O232 [最优控制];

学科分类号：

070105 ; 0711 ; 071101 ; 0811 ; 081101 ;

摘要：

We discuss the stochastic linear-quadratic(LQ) optimal control problem with Poisson processes under the indefinite case. Based on the wellposedness of the LQ problem, the main idea is expressed by the definition of relax compensator that extends the stochastic Hamiltonian system and stochastic Riccati equation with Poisson processes(SREP) from the positive definite case to the indefinite case. We mainly study the existence and uniqueness of the solution for the stochastic Hamiltonian system and obtain the optimal control with open-loop form. Then, we further investigate the existence and uniqueness of the solution for SREP in some special case and obtain the optimal control in close-loop form.

引用

页码：563 / 576

页数：14

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