搜索
报告题目：Stochastic Linear-Convex Problem and Classical Solution to HJB Equation
报 告 人：于志勇，山东大学 教授
报告摘要：In this talk, we are concerned with the classical solvability of a class of second-order Hamilton-Jacobi-Bellman equations (HJB equations) arising from stochastic optimal control problems with linear dynamics and uniformly convex cost functionals. By introducing the Hamiltonian system and extending the gradient descent method to a Hilbert space, we prove the existence and uniqueness of the optimal control under the uniform convexity condition. The regularity of the solution to the Hamiltonian system is obtained, including the derivatives with respect to the initial state and the Malliavin derivatives. The connection between the Hamiltonian system and the value function is subsequently proven, enabling us to derive regularity properties of the value function via probabilistic techniques. Finally, by the dynamic programming principle, the value function is verified to be the unique classical solution to the HJB equation and the optimal feedback control is provided. These results generalize the classical linear-quadratic theory and provide new insight into the regularity of the value function.
报告人简介：于志勇，山东大学数学学院教授，博士生导师。研究方向为随机控制与随机微分博弈、倒向随机微分方程、金融数学。在SIAM Journal on Control and Optimization, IEEE Transactions on Automatic Control, Automatica等学术期刊上发表论文40余篇。2014年获得山东省杰出青年基金，2019年入选山东大学杰出中青年学者，2021年获得教育部自然科学二等奖。
报告时间：2026年11月3日（星期二）上午9:30-12:30
报告地点：文渊楼B536
主办单位：数学与统计学院
学院宣传片
