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首页> 外文期刊>Frontiers of mathematics in China >Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games
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Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games

机译：平均场型前后双随机微分方程及相关随机差动游戏

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摘要

We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations, in which the coefficient contains not only the state process but also its marginal distribution, and the cost functional is also of mean-field type. It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions. We establish a necessary condition in the form of maximum principle and a verification theorem, which is a sufficient condition for Nash equilibrium point. We use the theoretical results to deal with a partial information linear-quadratic (LQ) game, and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation.
机译：我们研究了一种局部信息的偏心差分差动游戏的平均偏向双随机微分方程，其中系数不仅含有状态过程，还包含其边际分布，并且成本函数也是平均场类型。要求控制适应于由底层褐色运动产生的过滤的次过滤。我们以最大原则的形式和验证定理建立了必要条件，这是纳什均衡点的充分条件。我们使用理论结果来处理部分信息线性二次（LQ）游戏，并通过平均前向后向后的双随机微分方程的独特可解性获得LQ游戏问题的独特纳什均衡点。

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  • 来源
    《Frontiers of mathematics in China》 |2020年第6期|1307-1326|共20页
  • 作者

    Qingfeng ZHU; Lijiao SU; Fuguo LIU; Yufeng SHI; Yongao SHEN; Shuyang WANG;

  • 作者单位

    School of Mathematics and Quantitative Economics Shandong University of Finance and Economics and Shandong Key Laboratory of Blockchain Finance Jinan 250014 China Institute for Financial Studies and School of Mathematics Shandong University Jinan 250100 China;

    School of Mathematics and Quantitative Economics Shandong University of Finance and Economics and Shandong Key Laboratory of Blockchain Finance Jinan 250014 China;

    Department of Mathematics Changji University Changji 831100 China;

    Institute for Financial Studies and School of Mathematics Shandong University Jinan 250100 China;

    School of Mathematics and Quantitative Economics Shandong University of Finance and Economics and Shandong Key Laboratory of Blockchain Finance Jinan 250014 China;

    School of Informatics Xiamen University Xiamen 361005 China;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Non-zero sum stochastic differential game; mean-field; backward doubly stochastic differential equation (BDSDE); Nash equilibrium point; maximum principle;

    机译：非零和随机差动游戏;意思场;向后双随机微分方程（BDSDE）;纳什均衡点;最大原则;

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