报告题目：Optimal ratcheting of dividends with capital injection
报 告 人： 福建师范大学数学与统计学院 王文元 教授
报告时间：2024年3月30日下午3: 30 - 4: 30
报告地点：苏州大学本部览秀楼105学术报告厅
报告摘要: In this talk, I shall introduce a recent work of mine, which investigates the optimal dividend problem with capital injection and ratcheting constraint with non-decreasing dividend payout rate. Capital injections are introduced in order to eliminate the possibility of bankruptcy. Under the Cram\'er--Lundberg risk model, the problem is formulated as a two-dimensional stochastic control problem. By applying the viscosity theory, we show that the value function is the unique viscosity solution to the associated Hamilton-Jacobi-Bellman equation. In order to obtain analytical results, we further study the problem with finite ratcheting constraint, where the dividend rate takes only a finite number of available values. We show that the value function under general ratcheting can be approximated arbitrarily closely by the one with finite ratcheting. Finally, we derive the expressions of value function when the threshold--type finite ratcheting dividend strategy with capital injection is applied, and show the optimality of such strategy. Numerical examples under various scenarios are provided at the end.
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。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。目前主要研究兴趣为最优投资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 Math. Econom. / Scand. Actuar. J. / Eur. Actuar. J.，理论与应用概率期刊J. Theoret. Probab. / Adv. in Appl. Probab./ J. Appl. Probab. / Extremes，随机控制期刊J. Optim. Theory Appl. / Appl. Math. Opt. 等发表论文40余篇。主持国家自然科学基金项目3项。曾先后入选厦门市高层次人才（C类）、福建省新世纪优秀人才支持计划、福建师范大学宝琛计划。
