Financial Math Seminar

Optimal control with performance dependent dividend strategies and capital injection for spectrally negative Lévy risk processes

  • 演讲者:王文元(厦门大学)

  • 时间:2022-10-27 15:00-16:00

  • 地点:腾讯会议 ID 384-201-976,密码 221027

Abstract:Assume that the surplus process without dividend and capital injection for an insurance company evolves as a spectrally negative L\'evy process with the usual exclusion of negative subordinator or deterministic drift. Given $\ell_{2}\in(0,1)$ and $\ell_{1}\in(0,\ell_{2})$, dividends are distributed at some restricted fraction $\ell(\cdot)\in[\ell_{1},\ell_{2}]$ of the company's net income only when the company is in profitable situation, that is, the surplus process is at its running maximum. Meanwhile, the beneficiary of the dividends injects capital to ensure a non-negative risk process, so that the insurer never goes bankrupt. We consider the De Finetti's dividend problem of maximizing the difference between the expected discounted dividends and the expected discounted capital injection. The optimal value function and the optimal dividend strategy are obtained. It turns out that, corresponding to two opposite scenarios, the optimal dividend distribution rate keeps to be $\ell_{2}$ or switches from $\ell_{1}$ to $\ell_{2}$ once the surplus process hits some critical level and stays in the profitable situation. Some numerical examples are also provided. 


报告人简介:王文元,男,博士,厦门大学数学科学学院副教授、博士生导师。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。目前主要研究兴趣有马氏可加过程下的最优控制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领域杂志Insurance Math. Econom./Scand. Actuar. J./Eur. Actuar. J.,理论与应用概率领域杂志J. Theoret. Probab./Adv. in Appl. Probab./ J. Appl. Probab./Extremes,随机控制领域杂志 J. Optim. Theory Appl.等上发表科研论文 40 余篇。主持国家自然科学基金项目 3 项。2017 年入选福建省新世纪优秀人才支持计划。