报告题目： Optimal dividend problems under Sparre Andersen risk model
报告人：石家庄铁道大学副校长刘国欣教授
摘要：he optimal dividend problem has a long history in risk theory. The dividend problem under the Sparre Anderson models is much subtler due to its non-Markovian nature in general, and the literature is much more limited. It was listed as an open problem in Albrecher and Thonhauser (2009). In this talk, we focus on this problem. The approach used here is based on the theory of measure-valued generator of general PDMPs developed by Liu et al. (2017). We present the characterization of Markov controls and show that the dividend control is a Markov control if and only if the dividend control is an (predictable) additive functional of the controlled process. Furthermore, due to the special characterization of the additive functional of PDMPs (see, for example, Jacod and Skorokhod (1996), or Liu et al. (2017)), the characterization of a Markov control is analytic. With this characterization, the dynamic programming principle (DPP) and the associated dynamic programming equation (DPE) are derived. Specially, this DPE is a measure integro-differential equation in general. This implies that the value function in general is not necessarily Lipschitz continuous, even could have discontinuities. Though the DPP and DPE are derived with Markov control, the verification theorem is proved in content of all admissible controls. A short discussion is presented on the approaximation to optimal value function and followed with 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。
报告时间：2019年9月25日（周三）下午2:30-3:30
报告地点：9教326
欢迎感兴趣的老师和同学参加！
