Nonzero-sum impulse games with regime switching

：熊捷（南方科技大学）
：2023-05-05 14:00
：厦门大学海韵园实验楼105报告厅

报告人：熊捷（南方科技大学）

时  间：2023年5月5日14:00-15:00

地  点：厦门大学海韵园实验楼105报告厅

内容摘要:

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 a joint paper with Siyu Lv)

个人简介：

熊捷，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-2014年间，熊捷执教于美国田纳西大学数学系，在此期间，于2002-2003年在加拿大被授予随机过程与滤波Canada Research Chair；于2003-2004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。先后在《Annals of Probability》、《Probability Theory and Related Fields》、《Annals of Applied Probability》、《Annals of Statistics》、《Journal of Functional Analysis》、《Journal of Differential Equations》、《SIAM Journal on Control and Optimization》、《Automatica》、《IEEE Transactions on Automatic Control》、《Finance and Stochastics》等国际顶级刊物发表论文140余篇。

 

联系人：王文元