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A zero-sum hybrid stochastic differential game with impulse controls

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In this paper,we study a zero-sum stochastic differential game with the following salient features:(ⅰ)the system state is dictated by a hybrid diffusion,(ⅱ)both players use impulse controls,and(ⅲ)the game takes place on an infinite time horizon.First,the dynamic programming principle for the problem is proven.Then,the lower and upper value functions of the game are characterized as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman-Isaacs(HJBI)equation,which turns out to be a coupled system of variational inequalities with bilateral obstacles.Moreover,a verification theorem as a sufficient condition to identify a Nash equilibrium is established.The Nash equilibrium strategies for the two players,indicating when and how it is optimal to intervene,are given in terms of the obstacle part of the HJBI equation.

stochastic differential gameMarkov chainimpulse controlHJBI equationviscosity solutionverification theorem

Siyu LV、Zhen WU、Jie XIONG

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School of Mathematics,Southeast University,Nanjing 211189,China

School of Mathematics,Shandong University,Jinan 250100,China

Department of Mathematics and SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen 518055,China

2024

中国科学:信息科学(英文版)
中国科学院

中国科学:信息科学(英文版)

CSTPCDEI
影响因子:0.715
ISSN:1674-733X
年,卷(期):2024.67(11)