Lecture Content：

The lecture will delve into the optimal branching problem for a class of branching type diffusions, where the particles of the branching diffusion follow the trajectory of a Feller process. The exploration includes characterizing the value function by examining the corresponding viscosity solution. A branching type risk model is subsequently constructed. The lecture will also cover the optimal strategy for opening new businesses, supported by numerical examples.

Speaker Introduction:

Professor Junyi Guo is a professor and doctoral supervisor at the School of Mathematical Sciences, Nankai University, primarily engaged in the research of stochastic processes and their applications in finance and insurance. His early research focused on multi-index Markov processes and measure-valued Markov processes. He has co-authored two monographs, including "Modern Insurance Risk Theory," and published over 90 papers. Professor Guo has led numerous projects, including the National Natural Science Foundation of China, Sino-Russian exchange projects, and the Tianyuan Fund, and participated in EU FP7 Marie Curie Actions, National Basic Research Program of China (973 Program), and major projects of the National Natural Science Foundation of China. He has received the Jiaqing Miao MMPH Research Award from the Chinese Society for Mathematical, Mechanical, and Physical Studies on High Technology, the Eighth Tianjin Teaching Achievement Award, and has been recognized as an outstanding doctoral supervisor by Tianjin and Nankai University. He has served as Vice President of the Chinese Mathematical Society, President of the Tianjin Mathematical Society, Vice President of the Chinese Society for Probability and Statistics, and currently holds positions including Vice President of the Chinese Society for Interdisciplinary Sciences, Executive Director of the Chinese Society for Probability and Statistics, and editorial board member of the journal Insurance: Mathematics and Economics.