论文标题
具有状态切换和随机系数的非均匀随机LQ控制
Non-homogeneous stochastic LQ control with regime switching and random coefficients
论文作者
论文摘要
本文涉及一般的非均匀随机线性二次（LQ）控制问题，其制度切换和随机系数。我们从两个后向随机微分方程（BSDES）的系统方面获得了该问题的明确状态反馈控制和最佳值：一个是著名的随机riccati方程，而另一个是一个新的线性多维BSDE，所有系数都均为固定。 BMO Martingales和收缩映射方法证明了这两个BSDES的解决方案的存在和独特性。最后，该理论用于研究均值差异标准下的资产责任管理问题。
This paper is concerned with a general non-homogeneous stochastic linear quadratic (LQ) control problem with regime switching and random coefficients. We obtain the explicit optimal state feedback control and optimal value for this problem in terms of two systems of backward stochastic differential equations (BSDEs): one is the famous stochastic Riccati equation and the other one is a new linear multi-dimensional BSDE with all coefficients being unbounded. The existence and uniqueness of the solutions to these two systems of BSDEs are proved by means of BMO martingales and contraction mapping method. At last, the theory is applied to study an asset-liability management problem under the mean-variance criteria.
