报告题目：The Howard's Policy Iteration and Convergence for Optimal Dividend under Compound-Poission Model
时 间：2025年9月26日（星期五）14：30
地 点：腾讯会议：952916034
主 办：数学与统计学院
参加对象：感兴趣的老师和学生
报告摘要：This talk develops a novel entropy-regularized policy iteration algorithm (PIA)for solving the optimal dividend problem under the classical Compound-Poission risk model. Building on Howard’s classical PIA framework, we resolve longstanding barriers to policy iteration in dividend optimization: entropy regularization guarantees smooth PIA iterates, eliminating historical nonsmoothness obstacles;first-claim truncation transforms the governing integro-differential equation into an exactly solvable ODE system, overcoming spatial nonlocality; and boundedness arguments establish unique closed-form solutions without ad hoc boundary specifications. Furthermore, we prove uniform convergence of both value function sequences and associated policies – ensuring algorithmic stability under general compound Poisson dynamics. Finally, asymptotic analysis demonstrates consistency with classical theory: as λ→0+, our regularized solutions converge to the discontinuous bang-bang strategy and its value function. Collectively, this work establishes the first provably convergent implementation of Howard’s policy iteration algorithm (PIA) for Compound-Poission dividend models, resolving the tripartite challenges of nonsmoothness, nonlocality, and nonlinearity while preserving compatibility with classical control theory through vanishing entropy regularization.
报告人简介：柏立华，理学博士，南开大学数学科学学院教授、博士生导师。入选教育部新世纪优秀人才支持计划（2013）、天津市“131”创新型人才培养工程第二层次人选（2014）、天津市青年拔尖人才支持计划（2015）、天津市创新人才推进计划青年科技优秀人才（2017）。获全国优秀博士学位论文提名奖（2012）、天津市数学会青年学术奖一等奖（2017）。其主要研究方向包括随机过程、随机控制、精算数学、金融数学等。目前已经在AAP、SICON、FS、SPA、Bernoulli、JOTA、IME、Science China (A)、SAJ等主流期刊发表论文30余篇。作为项目负责人，主持国家自然基金面上项目3项，青年基金1项，天津市青年拔尖人才支持计划1项，南开大学“百名青年学科带头人培养计划”1项。