学术讲座

报告题目：An integral equation approach for optimal investment stopping problems with partial information

报告时间：2024年11月14日16:00

报告地点：湘江楼A927

报告人:马敬堂 教授

摘要：In this talk we present recent work on the study of a finite horizon optimal investment stopping problem with unobservable random variable for the return of risky asset.  Using the Bayesian filter and the dual control approach, we transform the original primal problem into a dual finite horizon optimal stopping problem, which results in the dual value function satisfying a variational inequality with two state variables. For a class of utility functions that include power utility and non-HARA utility, we show that the free boundary satisfies a Volterra type nonlinear integral equation with expectation over the joint distribution of the dual state process and the filtered probability process and we simplify and solve the integral equation with the dimension reduction and backward recursion methods. We also construct two simple closed-form approximations for the free boundary using its asymptotic properties and show their accuracy and efficiency with numerical examples. Furthermore, we demonstrate that different model parameters may lead to one, or two, or no free boundaries with a simple example. (This is joint work with Jie Xing and Harry Zheng.)

个人简介：西南财经大学数学学院、教授、博士生导师、院长，教育部新世纪优秀人才。现任四川省数学会副理事长，中国运筹学会理事，中国运筹学会金融工程与金融风险管理分会副理事长，East Asian Journal on Applied Mathematics副主编。主要研究方向为：计算数学、金融数学（期权定价模型、最优投资算法、随机控制计算、HJB方程数值解）。在SIAM Journal on Control and Optimization, European Journal of Operational Research, Insurance: Mathematics and Economics等期刊发表论文。