报告时间：2025年4月27日，15: 00-16: 00

报告地点：统计楼 106

报告题目： Optimal portfolio under ratio-type periodic evaluation in stochastic factor models under convex trading constraints

报告摘要：In this talk, we present a recent work on a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio of two adjacent wealth levels over an infinite horizon, featuring the dynamic adjustments in portfolio decision according to past achievements. Under power utility, we transform the original infinite horizon optimal control problem into an auxiliary terminal wealth optimization problem under a modified utility function. To cope with the convex trading constraints, we further introduce an auxiliary unconstrained optimization problem in a modified market model and develop the martingale duality approach to establish the existence of the dual minimizer such that the optimal unconstrained wealth process can be obtained using the dual representation. With the help of the duality results in the auxiliary problems, the relationship between the constrained and unconstrained models as well as some fixed point arguments, we derive and verify the optimal constrained portfolio process for the original problem over an infinite horizon.

报告人简介：王文元，男，博士，福建师范大学数学与统计学院教授、博士生导师、博士后合作导师。主要研究方向有保险金融数学、概率论与随机过程、随机控制与优化。目前主要研究兴趣是投资组合优化问题和基于机器学习的随机控制问题。近年来以第一或通讯作者身份在保险精算期刊Insurance: Mathematics and Economics/Scandinavian Actuarial Journal/European Actuarial Journal，运筹学期刊Mathematics of Operations Research，随机控制期刊Applied Mathematics and Optimization/Journal of Optimization Theory and Applications，理论与应用概率期刊Journal of Theoretical Probability/Advances in Applied Probability/Journal of Applied Probability/Extremes等上发表论文50余篇。主持国家自然科学基金项目多项。曾先后入选厦门市高层次人才、福建省新世纪优秀人才支持计划、福建师范大学高端人才计划等。