教育部人文社科重点研究基地中央财经大学中国精算研究院学术活动
精算论坛第254期讲座
(2024年12月20日)
讲座主题一：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 theinjected capital always dominates the benchmark process. The stochastic control problem isto maximize the expected utility of consumption deducted by the cost of the capital injectionunder the dynamic floor constraint. By introducing two auxiliary state processes with reflections, an equivalent auxiliary control problemis formulated and studied, which leads to the HJB equation with two Neumann boundary conditions. We establish the existence of a uniqueclassical solution to the dual PDE using some novel probabilistic representations involving thelocal time of some dual processes together with a tailor-made decomposition-homogenizationtechnique. The proof of the verification theorem on the optimal feedback control can be carriedout by some stochastic flow analysis and technical estimations of the optimal control.
报告人一：
薄立军，理学博士，西安电子科技大学数学与统计学院教授，概率与数理统计专业博士生导师。2012年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青年项目1项、面上项目2项、中科院前沿科学重点研究计划-青年拔尖科学家项目；获陕西省工业与应用数学学会首届青年科技奖(2019年)和2023年度陕西高等学校科学技术研究优秀成果奖特等奖(第一完成人);在概率统计、随机控制和金融数学等领域权威学术期刊发表SCI和SSCI检索论文70余篇。代表性论文发表的主要期刊包括：《The Annals of Applied Probability》、《SIAM Journal on Financial Mathematics》、《Stochastic Processes and their Applications》、《Production and Operations Management》、《Mathematical Finance》、《SIAM Journal on Control & Optimization》、《Mathematics of Operations Research》、《Insurance: Math. & Econ.》、《Applied Mathematics and Optimization》、《Finance and Stochastics》、《Journal of Banking and Finance》、《Journalof Economic Dynamics and Control》和《Quantitative Finance》等。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(AIMS)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。目前聚焦于残差深度学习、金融交互系统和模仿变异动力学的随机控制问题。 出版教材《随机过程》、《哈佛概率公开课》（译著）、《最优化模型》（译著）和《高等概率论》（科学出版社“十四五”高等学校本科规划教材）。
讲座主题二：Robust optimal investment and benefit adjustment strategy for target benefit pension plan with ambiguity in stochastic environments
摘要：This paper studies robust optimal investment and benefit adjustment strategy for the target benefit pension (TBP). Assuming that the fund manager is ambiguity-averse which is caused by model uncertainty and is allowed to invest pension funds in the financial market containing a risk-free asset, a risky asset (a stock) and a zero-coupon bond. Supposing that the instantaneous interest rate of the risk-free asset is obedient to the affine interest rate model. The price process of the risky asset is driven by 4/2 stochastic volatility model with stochastic interest rate. The weighted product of pension wealth and benefit payment is taken into account in the objective function with the form of Cobb-Douglas utility function. Applying stochastic optimal control theory, homologous Hamilton-Jacobi-Bellman (HJB) equation is built and then explicit solutions of robust optimal investment and benefit adjustment strategy are deduced. Finally, numerical examples are given to illustrate the results obtained.
报告人二：
常浩，天津工业大学教授，博士生导师。研究方向：数理金融；保险精算；风险管理与精算。主持（完成）国家社科基金后期资助项目等纵向项目7项。以第一作者和通讯作者先后在Insurance: Mathematics and Economics、Economic Modelling、Optimization等国内外核心刊物发表论文60余篇，其中SCI、SSCI和EI收录30余篇，出版专著1部。天津市高校“中青年骨干创新人才支持计划”人选，天津大学博士及博士后，教育部第五轮学科评估函评专家（统计学科），教育部学位中心学位论文评议专家，国家社科基金项目成果通讯鉴定专家，担任中国现场统计研究会大数据统计分会等分会理事，国内外20余个核心期刊审稿专家。
讲座时间：2024年12月20日（周五）
下午14:00-16:30
报告地点：腾讯会议768-433-511
邀 请 人：韦晓 伍慧玲
