题目：A Class of Stochastic Control Problems Arising from Relaxed Benchmark Tracking
    摘要：This talk discusses stochastic control problems motivated by optimal consumption with wealth benchmark tracking. The benchmark process is modeled by a combination of a geometric Brownian motion and a running maximum process, 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 of 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.

报告人简介：薄立军，教授。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青年、面上、中科院前沿科学重点以及陕西国家应用数学中心交叉团队培育项目等。目前已在Ann. Appl. Probab.、Math. Finan.、Stoch. Process. Appl.、SIAM J. Contr. Optim.、SIAM J. Finan. Math.、Math. Opers. Res.、J. Banking Finan.等学术期刊发表学术论文60余篇，出版本科和研究生教材四部。

时间地点： 11月21号14：00  腾讯会议 882-309-921