带Markov切换参数的线性二次零和随机微分博弈

朱怀念,植璟涵,张成科,宾宁

系统科学与数学 ›› 2013, Vol. 33 ›› Issue (12) : 1391-1403.

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系统科学与数学 ›› 2013, Vol. 33 ›› Issue (12) : 1391-1403. DOI: 10.12341/jssms12215
论文

带Markov切换参数的线性二次零和随机微分博弈

    朱怀念,植璟涵,张成科,宾宁
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LINEAR QUADRATIC ZERO-SUM STOCHASTIC DIFFERENTIAL GAMES WITH MARKOV REGIME SWITCHING

    ZHU Huainian, ZHI Jinghan ,ZHANG Chengke , BIN Ning
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摘要

研究了一类连续时间带Markov切换参数的线性二次零和随机微分博弈问题, 在广义It\^{o}微分的意义下,通过引入一个广义Riccati微分(或者代数)方程证明了该广义Riccati方程的可解性是相应随机微分博弈问题均衡策略存在的一个充分必要条件,同时给出了最优策略闭环形式的显式解以及最优性能指标值,最后给出了数值算例验证结论的正确性.

Abstract

In this paper, we discuss the problem of a class of linear quadratic zero-sum stochastic differential games with Markov regime switching in continuous time. Under the  condition of generalized It\^{o}'s differential rule, by  introducing a generalized Riccati differential (algebraic) equation,  it is proved that the solvability of the associated generalized Riccati  equation is both sufficient and necessary condition for the existence   of equilibrium strategies, meanwhile, the explicit solution of equilibrium strategies with closed form and the optimal value of cost functional are obtained. Fi ally, a numerical example is given to illustrate the validity of the obtained results.

关键词

  / 随机系统, Markov切换参数, 微分博弈, 广义Riccati方程.

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朱怀念,植璟涵,张成科,宾宁. 带Markov切换参数的线性二次零和随机微分博弈. 系统科学与数学, 2013, 33(12): 1391-1403. https://doi.org/10.12341/jssms12215
LINEAR QUADRATIC ZERO-SUM STOCHASTIC DIFFERENTIAL GAMES WITH MARKOV REGIME SWITCHING. Journal of Systems Science and Mathematical Sciences, 2013, 33(12): 1391-1403 https://doi.org/10.12341/jssms12215
中图分类号: 91A23   
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