Time-inconsistent Linear-quadratic Non-zero Sum Stochastic Differential Games with Random Jumps and Applications

嘉宾：吴臻教授

邀请人：彭云飞教授

时间：2024年10月8日 19:30-20:30

地点：腾讯会议（会议号：797393969）

主办单位：贵州大学数学与统计学院

个人简介

吴臻，山东大学数学学院教授，教育部“长江学者”特聘教授，国家杰出青年基金获得者，泰山学者攀登计划专家。现任山东大学副校长兼数学学院院长，中国数学会副理事长，国家自然科学基金委员会数理学部第九届专家咨询委员会委员，教育部大学数学教学指导委员会委员，山东数学会理事长，研究领域涉及控制论、概率论和金融数学等，取得了一系列具有突破性和原创性的科研成果，曾任国际控制理论权威期刊SIAM J. Control Optim.编委，现任国家基金委英文期刊Fundamental Research 数学物理领域编委，SCI 学术期刊ESAIM-Control Optim. Calc. Var.、Statist. Probab. Lett.、国际学术期刊Probab. Uncertain. Quant. Risk 和Part. Diff.Equa. Appl.编委。曾获中国数学会第十七届陈省身数学奖，首位获山东省自然科学奖一等奖，作为主要完成人5次获得国家教学成果奖，获首届国家优秀教材二等奖，2次获山东省教学成果特等奖。主持国家重点研发计划项目、国家基金委重点项目、山东省重大基础研究项目等。为国家“万人计划”首批科技创新领军人才入选者和科技部首批国家创新人才推进计划 “金融数学”重点领域创新团队负责人，入选国家百千万人才工程并获得“有突出贡献中青年专家”荣誉称号，享受国务院政府特殊津贴。

Abstract

 In this talk, we discuss a kind of time-inconsistent linear-quadratic (LQ) non-zero sum stochastic differential game (NZSSD) problems with random jumps and its applications. We first introduce the background of time-inconsistency by two examples. Then we mainly formulate a time-inconsistent LQ NZSSDG problem with random jumps and give an appropriate definition of Nash equilibrium point in the open-loop form. We derive a general sufficient condition for Nash equilibrium point through a flow of FBSDEs with random jumps and give a Nash equilibrium point explicitly by solutions of some Riccati-like and linear ODEs when the state is one-dimensional and all coefficients are deterministic. As an application, we also study a time-inconsistent corporate international investment problem with discontinuous cash flow and give an equilibrium solution. We finally present several simulating examples to show the influence of some market parameters on the equilibrium strategy. This talk is mainly based on the works ofH. Wang and Z. Wu (2022) , International Journal of Control, 95(7) and H. Wang and Z. Wu (2023), Commun. Math. Sci., 21(7).