讲座题目：Optimal State Equation for the Control with Two Distinct Dynamic Systems
主讲人：吴盼玉 教授
主持人：李丹萍 教授
开始时间：2025-12-16 09:00
讲座地址：普陀校区理科大楼A1714
主办单位：统计学院
报告人简介：
吴盼玉，山东大学金融研究院教授，博士生导师，山东大学未来计划青年学者，山东省大数据研究会理事。主要从事非线性概率与期望、倒向随机微分方程理论及应用、金融数学等领域的研究，论文发表在IEEE TAC，Automatica，Stoch. Proc. Appl.，Sci. China Math.等国内外知名期刊上，获山东省高等学校科学技术奖二等奖。主持国家自然科学基金、山东省自然科学基金、博士后基金等多项科研项目，作为骨干成员参加国家重点研发计划和山东省自然科学基金重大基础研究项目。
报告内容：
We consider a class of stochastic control problems which have been widely used in optimal foraging theory and financial modeling. The optimal state process has two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether it takes values bigger or smaller than a threshold value. Adopting a perturbation type approach, we find an expression for potential measure of the optimal state process. We then obtain an expression for the transition density of the optimal state process by inverting the associated Laplace transform. Properties including the stationary distribution of the optimal state process are discussed. Finally, an expression of the value function and the optimal control are given for such stochastic control problems. As an application, we transform the continuous-time two-armed bandit problem in finance into our control framework to derive the optimal investment strategy which maximizes the probability of reaching a specified threshold.
