题目：Hybrid optimal impulse control

摘要：This talk is concerned with an optimal impulse control problem under a hybrid diffusion (or, regime switching) model, where the state of the system consists of a number of diffusions coupled by a continuous-time finite-state Markov chain. The objective is to minimize the expected discounted cost from exerting the impulse control in the infinite horizon. Based on the dynamic programming principle (DPP), the value function of the hybrid optimal impulse control problem is shown to be the unique viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, which is in the form of a coupled system of variational inequalities. Moreover, a verification theorem as the sufficient condition for optimality of a solution is also established. The optimal impulse control, indicating when and how it is optimal to intervene, is described by the obstacle part of the HJB equation. Finally, the general theoretical results are applied to an optimal cash management problem. The value function in closed-form and an explicit optimal policy are obtained, which exhibit clearly the effect of regime switching on the agent's decision. This talk is based on a joint work with Prof Jie Xiong.

主讲人简介：吕思宇，东南大学数学学院硕士生导师，东南大学至善青年学者。2017年在山东大学数学学院获得博士学位。2015年至2016年在美国佐治亚大学数学系访问学习。多次到香港理工大学、香港城市大学、南方科技大学、复旦大学等合作研究。主要研究领域为混合随机系统的最优控制和微分对策理论及其在金融中的应用，取得了以动态规划方法为特色的创新性成果，在国内外重要学术期刊Automatica、Annals of Operations Research、Chinese Annals of Mathematics, Series B等发表多篇论文，并主持多项国家级和省部级科研项目。

邀请人：于志勇，数学学院教授

时间：9月23日（周五）9:30-10:30

地点：腾讯会议

联系人：于志勇，联系方式：yuzhiyong@sdu.edu.cn