数学与统计学院学术报告[2023] 019号

(高水平大学建设系列报告790号)

报告题目: Optimal ratcheting of dividends with capital injection

报告人：徐冉

报告时间：2023.04.18 15:00-16:00pm

讲座地点：腾讯会议289 637 790

报告内容：In this paper, we investigate the optimal dividend problem with capital injection and ratcheting constraint on the dividend payout rate, that is, the dividend payment process is absolutely continuous with non-decreasing dividend rate through the lifetime of the company. Capital injections with proportional transaction costs are introduced in order to eliminate the possibility of bankruptcy. Under the Cramér-Lundberg risk model, the problem is formulated as a two-dimensional stochastic optimal control problem. By applying the viscosity theory, we show that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation within certain functional class. However, analytical results of the value function and corresponding optimal strategy is rather difficult to obtain for general claim size distribution and general ratcheting of dividend strategy. Hence, in turn, we study the optimal dividend and capital injection problem with finite ratcheting, where the finite ratcheting refers to the case when dividend rate takes only finite number of available values. With a convergence analysis, we show that the value function under general ratcheting constraint can be approximated arbitrarily closely by the ones with finite ratcheting assumption. Finally, under exponential claim size and finite ratcheting constraint, we derive analytical expressions for the value function when the threshold-type dividend strategies with capital injection are applied, and show that the optimal finite ratcheting strategy can be identified within such type.

报告人简历：徐冉，西交利物浦大学数学物理学院金融与精算数学系助理教授，18年获得香港大学统计精算系博士学位，18-19年在加拿大康考迪亚大学从事博士后研究工作，19年9月加入西交利物浦大学，主要研究方向为保险精算、风险理论、金融保险中的随机最优化问题。目前主持国家自然科学基金青年项目一项，参与国家自然科学基金面上项目一项。相关研究成果发表于Insurance: Mathematics and Economics, European Journal of Operational Research, Journal of Computational and Applied Mathematics, Probability in the Engineering and Informational Sciences等国际期刊。

　数学与统计学院

                                                2023年04月12日