建院40周年系列活动之学术讲座第十期
统计学系列Seminar第67期
主题: Optimal Tracking Portfolio with A Ratcheting Capital Benchmark
主讲人：薄立军
主持人：王国长
会议平台：腾讯会议（会议ID: 150 698 142）
会议时间：2020年9月17日下午14:00-15:00
摘要: This talk is concerned with the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. To formulate such an optimal tracking problem, we envision that the fund manager can dynamically inject capital into the portfolio account such that the total capital dominates the nondecreasing benchmark floor process at each intermediate time. The control problem is to minimize the cost of the accumulative capital injection. We first transform the original problem with floor constraints into an unconstrained control problem, however, under a running maximum cost. By identifying a controlled state process with reflection, we next transform the problem further into an equivalent auxiliary problem, which leads to a nonlinear Hamilton-Jacobi-Bellman (HJB) with a Neumann boundary condition. By employing the dual transform, the probabilistic representation approach and some stochastic flow arguments, the existence of the unique classical solution to the dual HJB is established. The verification theorem is carefully proved, which gives the complete characterization of the primal value function and the feedback optimal portfolio.
主讲人简介
薄立军，教授，本科毕业于西安电子科技大学数学系，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。 2012年入选教育部新世纪优秀人才支持计划，先后主持国家自然科学基金面上项目2项 (数理学部)、中科院前沿科学重点研究计划-青年拔尖科学家项目。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Math. Finan., Finan. & Stoch., SIAM J. Finan. Math., SIAM J. Control & Optim, Math. Opers. Res., J.Banking & Finan., Appl. Math. & Optim., J. Dyn. Econ. & Contr., Queueing Syst., J. Theor. Probab.上发表学术论文30余篇。目前担任中国概率统计学会会刊《应用概率统计》编委；美国数学科学研究所(AIMS)旗舰期刊《J. Dynamics & Games》Associate Editor。
