摘要: In this talk we study open-loop and closed-loop solvabilities for stochastic linear quadratic (LQ) optimal control problems. A simple example shows that these two solvabilities are different. It is proved that convexity of the cost functional is necessary for the open-loop solvability of the problem, whereas uniform convexity of the cost functional is sufficient.By considering a family of uniformly convex cost functionals, a minimizing sequence, whose convergence is equivalent to the open-loop solvability, is constructed.Then, we establish the key result that the uniform convexity of the cost functional is equivalent to the strongly regular solvability of the corresponding Riccati equation.Further, closed-loop solvability is established by means of regular solvability of the Riccati equation, and finiteness of the LQ problem is characterized by the convergence of the solutions to a family of Riccati equations.  

报告人简介：Dr. Jingrui Sun received his Ph.D. degree in Mathematics from University of Science and Technology of China in 2015. He is currently a Postdoctoral Fellow at the Hong Kong Polytechnic University. His main research interests are stochastic control theory, differential games, and mathematical finance. In the past two years, he has published several papers in journals such as SIAM Journal on Control and Optimization and ESAIM: Control, Optimisation and Calculus of Variations.