Maximum Principle for Non-Zero Sum Stochastic Differential Game with Discrete and Distributed Delays

被引：0
作者：
Qixia Zhang
机构：
[1] University of Jinan,School of Mathematical Sciences
来源：
Journal of Systems Science and Complexity | 2021年 / 34卷
关键词：
Distributed delay; generalized anticipated backward stochastic differential equations; maximum principle; Nash equilibrium point; non-zero sum stochastic differential game;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays. Not only the state variable, but also control variables of players involve discrete and distributed delays. By virtue of the duality method and the generalized anticipated backward stochastic differential equations, the author establishes a necessary maximum principle and a sufficient verification theorem. To explain theoretical results, the author applies them to a dynamic advertising game problem.
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页码：572 / 587
页数：15
相关论文
共 37 条
  • [1] Nash J(1951)Non-cooperative games Ann. Math. 54 286-295
  • [2] Buckdahn R(2004)Nash equilibrium payoffs for nonzero-sum stochastic differential games SIAM J. Control Optim. 43 624-642
  • [3] Cardaliaguet P(2003)BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations Stoc. Proc. Appl. 107 145-169
  • [4] Rainer C(2012)A partial information non-zero sum differential game of backward stochastic differential equations with applications Automatica 48 342-352
  • [5] El Karoui N(2007)A delayed Black and Scholes formula Stoc. Annal Appl. 25 471-492
  • [6] Hamadéne S(2015)Verification theorem of stochastic optimal control with mixed delay and applications to finance Asian J. Control 17 1285-1295
  • [7] Wang G C(2017)Maximum principle for partially-observed optimal control problems of stochastic delay systems Journal of Systems Science & Complexity 30 316-328
  • [8] Yu Z Y(2017)Control for Itô stochastic systems with input delay IEEE T. Automat. Contr. 62 350-365
  • [9] Arriojas M(2009)Anticipated backward stochastic differential equations Ann. Probab. 37 877-902
  • [10] Hu Y(2010)Maximum principle for the stochastic optimal control problem with delay and application Automatica 46 1074-1080
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