报告题目：Optimal dividend problem for Cramér-Lundberg model under transaction costs

报告人：刘国欣 （石家庄铁道大学）

报告时间：2021年5月17日上午11:00-12:00

报告地点：数学院145报告厅

报告摘要：In this paper, we focus on the optimal dividend problem under the Cram´erLundberg model under transaction costs and try to present a formal description of the optimal strategy and provide a policy iteration algorithm with rigorous numerical analysis. In order to do so, an auxiliary optimization problem is introduced by maximizing dividend payment with terminal reward up to the arrival-time of the first claim. The auxiliary optimization problem is solved completely in the sense that, no matter what the claimsize distribution is, the explicit formulas for both optimal strategy and value function are presented. Since the optimal dividend problem can be seen as a special case of the auxiliary optimization problem, these formulas provide a description of the optimal strategy. We show that the optimal value function is a nonnegative solution of an optimal equation. So, in any case, it can be approximated by iteration algorithm starting with the initial zero-valued policy, the policy of no dividend payment at all. These establish a rigorous numeral analysis for the policy iteration algorithm. Finally, the algorithm is explained by numerical examples.

报告人简介：刘国欣，石家庄铁道大学教授,副校长。1993年破格晋升副教授；1996年破格晋升教授。1998年6月毕业于长沙铁道学院概率论与数理统计专业，获理学博士学位，师从著名数学家侯振挺教授研究马氏骨架过程，获湖南省首届优秀博士论文奖。上世纪90年代初刘国欣教授主要从事概率论极限定理的研究工作，在非齐次马氏链泛函的强大数定律及条件三级数定理研究中取得了重要进展。1995年对马氏骨架过程中重要的一类——逐段决定马氏骨架过程的研究作了基础性的工作；为逐段决定马氏过程的研究奠定了全新的起点和新的理论基础。主要研究成果汇集于与侯振挺教授合著的专著《Markov Skeleton Processes and their Applications》。近年来，刘国欣教授研究重点转向保险风险问题驱动的逐段决定马氏过程理论的研究。刘国欣教授主持完成国家自然科学基金项目3项。在Stochastic Processes and their Application, Insurance: Mathematics and Economics, Scandinavian Actuarial Journal, Science China: Mathematics, Statistics and Probability Letters等重要期刊发表论文30余篇，著作3部。2007年获天津市五一劳动奖章。现兼任中国工程概率统计学会理事长、河北省数学会理事长。