讲座题目：The Howard's Policy Iteration and Convergence for Optimal Dividend under Compound-Poission Model
主讲人：柏立华 教授
主持人：危佳钦 教授
开始时间：2025-10-17 09:30
线上会议会议号：131318814 密码：705614
主办单位：统计学院
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、天津市青年拔尖人才支持计划、天津市创新人才推进计划青年科技秀人才。获全国优秀博士学位论文提名奖、天津市数学会青年学术奖一等奖。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Annals of Applied Probability、SIAM J. Control Optim.、Finance Stoch.、Stoch. Proc. Appl.、Bernoulli、J optim. theory appl、App Math Optima、Quant. Finance、Scand. Actuarial J.、Insurance: Math. Econ.等主流期刊发表论文20余篇。
报告内容：
This paper 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 longstand\u0002ing 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 bounded\u0002ness 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 consis\u0002tency 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 pol\u0002icy 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.
