数学科学学院学术报告[2024] 055号

(高水平大学建设系列报告935号)

报告题目: Optimal dividend and capital injection control for a killed jump–diffusion process with two–sided jumps

报告人：徐冉，副教授，西交利物浦大学

报告时间：2024.06.28 09:00-10:00am

讲座地点：汇星楼（科技楼）514

报告内容：In this paper, we study the optimal dividend and capital injection control with terminal payment at ruin under the dual jump–diffusion process with two–sided jumps and killed exponentially. Unlike the usual assumption in the literature, we further relax the constraint on capital injection control and assume that the decision–maker can choose to inject capital or declare ruin when the surplus becomes negative. We derive the dynamic programming principle and quasi-variational inequations (QVIs) for such an optimal control problem. Due to the complexity of such a problem, we apply the Markov chain approximation method to solve it numerically, where we introduce a discrete–time controlled Markov chain that is locally consistent with the controlled dual jump–diffusion process, and design the corresponding numerical algorithm with value iteration to identify the optimal value function and an optimal control strategy. A convergence analysis for the approximation is provided based on the theory of weak convergence. Some numerical examples are given at the end when the jumps follow a double exponential distribution.

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副教授，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。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。

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邀请人：李婧超

　　　　　　　　　　　　　　　　　　数学科学学院

　　　　　　　　　　　　　　　　　2024年06月25日