论文标题
具有预期路径约束和相关约束FBSDE的SDE的最佳控制
Optimal control of SDEs with expected path constraints and related constrained FBSDEs
论文作者
论文摘要
在本文中，我们考虑对受期望路径约束的随机微分方程的最佳控制。根据受约束的FBSDE，给出了一般最佳随机控制的随机原理。特别是，我们伴随方程式中的补偿过程是确定性的，在文献中似乎是新的。对于典型的线性随机系统和二次成本函数（即所谓的LQ最佳随机控制），建立了验证定理，并给出了约束反射的FBSDE的存在和独特性。
In this paper, we consider optimal control of stochastic differential equations subject to an expected path constraint. The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs. In particular, the compensated process in our adjoint equation is deterministic, which seems to be new in the literature. For the typical case of linear stochastic systems and quadratic cost functionals (i.e., the so-called LQ optimal stochastic control), a verification theorem is established, and the existence and uniqueness of the constrained reflected FBSDEs are also given.
