时 间：2026年1月12 日（周一）14：00 – 15：00
地 点：腾讯会议号: 661-928-461 会议密码: 206185
报告人：薄立军 西安电子科技大学教授
主持人：李丹萍 华东师范大学教授
摘 要：
This talk discusses the Merton's optimal portfolio and consumption problem in an extended formulation by incorporating the benchmark tracking on the wealth process. We consider a tracking formulation such that the wealth process compensated by a fictitious capital injection outperforms the benchmark at all times. The fund manager aims to maximize the expected utility of consumption deducted by the cost of the capital injection, where the latter term can also be interpreted as the expected largest shortfall of the wealth with reference to the benchmark. By considering an auxiliary state process, we formulate an equivalent stochastic control problem with state reflections at zero. For general utility functions and Ito's diffusion benchmark process, we develop a convex duality theorem, new to the literature, to the auxiliary stochastic control problem with state reflections in which the dual process also exhibits reflections from above. For CRRA utility and geometric Brownian motion benchmark process, we further derive the optimal portfolio and consumption in feedback form using the new duality theorem, allowing us to discuss some interesting financial implications induced by the additional risk-taking from the capital injection and the goal of tracking.
报告人简介：
薄立军，西安电子科技大学教授，博士生导师，西安电子科技大学数学与统计学院执行院长。研究方向为随机分析、随机控制与金融数学。在概率统计、随机控制和金融数学等领域权威学术期刊《Ann. Appl. Prob.》《Math. Oper. Res.》《Production Oper. Manag.》(UTD 24)《Math. Finan.》《Science China: Math.》《SIAM J. Contr. Optim.》《SIAM J. Finan. Math.》等SCI和SSCI检索论文70余篇，出版本科和研究生教材四部。入选教育部新世纪优秀人才支持计划、陕西国家应用数学中心交叉团队负责人、陕西省杰青；主持国家自然科学基金项目4项、陕西数理基础科学研究重点项目、中科院前沿科学重点研究计划-青年拔尖科学家项目。目前担任中国工程概率统计学会副理事长、陕西省工业与应用数学学会副理事长、美国数学科学研究所旗舰期刊《Journal of Dynamics and Game》和中国概率统计学会会刊《应用概率统计》编委。研究成果获陕西省工业与应用数学学会首届青年科技奖、陕西高校科学技术研究优秀成果奖特等奖、陕西省自然科学二等奖。