深圳大学四十周年校庆暨数学学科四十周年庆

荔园学者Colloquium第三十一期

讲座题目:Hybrid Impulse Control and Game

主讲人：熊捷 教授（南方科技大学）

讲座时间：2023年6月19日8：00-9：00

讲座地点：深圳大学粤海校区国际会议厅大厅

内容概述：This talk is concerned with a two-player nonzero-sum stochastic differential game, where both players use impulse controls and the state process evolves as a regime switching diffusion. Based on a system of variational inequalities (VIs), a verification theorem as a sufficient criterion for optimality is established. Nash equilibrium strategies for the two players, indicating when and how it is optimal to intervene, are given in terms of the obstacle parts of the VIs. An important yet rather subtle issue is how to set an appropriate regularity condition for the solutions to the VIs, which together with the so-called smooth-fit principle lead to a suitable system of algebraic equations. As an application of the theoretical results, an example of exchange rate game between two countries is provided. By taking advantage of the verification theorem, a Nash equilibrium and the corresponding value functions are explicitly constructed. It is shown in this talk that involving the Markov chain in the problem actually makes a significant difference from the case where there is no regime switching.This talk is based on two joint papers with Siyu Lv.

主讲人简介：熊捷教授，1983年在北京大学数学系获得学士学位，1986年获得北京大学概率统计系硕士学位，1992年在美国北卡罗莱纳大学教堂山分校统计系获得博士学位。1992年至2014年间，熊捷执教于美国田纳西大学数学系，在此期间，于2002年至2003年在加拿大被授予随机过程与滤波Canada Research Chair；于2003年至2004年获得洪堡奖学金并赴德国进行合作研究。2014年正式入职澳门大学数学系，并于2017年底作为讲席教授加入南方科技大学数学系。他的研究领域包括：随机滤波和控制，数理金融，数理生物，测度值随机过程以及随机偏微分方程。

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                                            　数学与统计学院

2023年06月15日