报告人：薄立军
报告地点：腾讯会议ID:533364347
报告时间：2023年12月07日星期四14:00-15:00
邀请人：刘秉辉
报告摘要：
This talk discusses a stochastic control problem motivated by the optimal consumption with wealth benchmark tracking. The benchmark process is assumed to be a combination of a geometric Brownian motion and the running maximum process of a drifted Brownian motion, indicating its increasing trend in the long run. We consider a relaxed tracking formulation such that the wealth compensated by the injected capital always dominates the benchmark process. The stochastic control problem is to maximize the expected utility on consumption deducted by the cost of the capital injection under the dynamic floor constraint. By introducing two auxiliary state processes with reflections, an equivalent auxiliary control problem is formulated and studied, which leads to the HJB equation with two Neumann boundary conditions. We establish the existence of a unique classical solution to the dual PDE using some novel probabilistic representations involving the local time of some dual processes together with a tailor-made decomposition homogenization technique. The proof of the verification theorem on the optimal feedback control can be carried out by some stochastic flow analysis and technical estimations of the optimal control.
主讲人简介：
薄立军，西安电子科技大学数学与统计学院院长，教授、博士生导师。本科毕业于西安电子科技大学、硕士和博士毕业于南开大学概率论与数理统计专业，研究方向为随机分析、随机控制与金融数学。先后主持国家自然科学基金面上项目、中科院前沿科学重点研究计划-青年拔尖科学家项目、陕西国家应用数学中心交叉团队培育项目等。目前已在国际公认的概率统计、金融数学、管理和运筹学权威期刊Ann. Appl. Probab.、Stoch. Process. Appl. 、Math. Finan.、SIAM J. Contr. Optim.、SIAM J. Finan. Math.、Math. Opers. Res.、Prod. Oper. Manag. (POM)上发表学术论文70余篇，出版本科和研究生教材四部。
