报告题目: The tracking portfolio optimization
时 间：2022年12月8日（星期四）下午14：30
地 点：腾讯会议（ID：427-746-641）
主 办：数学与统计学院
参加对象：统计系老师与学生
报告摘要：This talk considers a portfolio management problem by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject capital into the portfolio account such that the total capital dominates a nondecreasing benchmark floor process at each intermediate time. The tracking problem is formulated to minimize the cost of accumulated capital injection. We first transform the original problem with floor constraints into an unconstrained control problem, but under a running maximum cost. By identifying a controlled state process with reflection, the problem is further shown to be equivalent to an auxiliary problem, which leads to a nonlinear HJB equation with a Neumann boundary condition. By employing the dual transform, the probabilistic representation, and some stochastic flow analysis, the existence of a unique classical solution to the HJB equation is established. The verification theorem is carefully proved, which gives a complete characterization of the feedback optimal portfolio. The application to market index tracking is also discussed when the index process is modeled by a geometric Brownian motion.
报告人简介：薄立军，教授、博导。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。先后主持教育部新世纪优秀人才支持计划项目、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.、Insurance: Math. Econom.、J. Banking Finan.上发表学术论文60余篇，出版本科和研究生教材四部。