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时滞随机系统的微分博弈理论及应用 经济管理类;专著;微分学;对策论 VIP

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丛书名:
朱怀念   社会科学文献出版社  2019-01 出版
ISBN:978-7-5201-4078-2

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该书以工程和经济金融领域中广泛使用的时滞随机系统为研究对象,利用动态优化理论中的随机最大值原理和动态规划等方法,系统研究时滞随机系统的微分博弈问题,得到了博弈系统的鞍点均衡策略、纳什均衡策略、Stackelberg均衡策略及Pareto均衡策略的存在条件和显式表达,并将所得结果应用于现代鲁棒控制理论中的随机H2/H∞控制以及数理金融中的投资与消费选择问题,丰富了博弈论的相关研究。
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  • 前言
  • 符号说明
  • 第1章 绪论
    1. 1.1 研究背景与意义
    2. 1.2 国内外研究现状综述
    3. 1.3 研究方法与技术路线
  • 第2章 时滞线性随机系统的Nash微分博弈
    1. 2.1 引言
    2. 2.2 时滞随机系统的LQ问题
    3. 2.3 有限时间Nash博弈
    4. 2.4 无限时间Nash博弈
    5. 2.5 时滞线性随机系统的零和博弈
    6. 2.6 本章小结
  • 第3章 时滞线性随机系统的Stackelberg博弈
    1. 3.1 引言
    2. 3.2 问题描述
    3. 3.3 无时滞博弈问题
    4. 3.4 带时滞博弈问题
    5. 3.5 本章小结
  • 第4章 时滞线性随机系统微分博弈的Pareto策略
    1. 4.1 引言
    2. 4.2 无时滞博弈问题的Pareto策略
    3. 4.3 带时滞博弈问题的Pareto策略
    4. 4.4 本章小结
  • 第五章 基于Nash博弈的时滞线性系统随机/控制
    1. 5.1 引言
    2. 5.2 无时滞线性系统的随机/控制
    3. 5.3 时滞线性系统的有限时间随机/控制
    4. 5.4 时滞线性系统的无限时间随机/控制
    5. 5.5 本章小结
  • 第6章 广义时滞线性随机系统的多人Nash微分博弈
    1. 6.1 引言
    2. 6.2 无时滞广义线性随机系统的Nash微分博弈
    3. 6.3 广义时滞线性随机系统的Nash微分博弈
    4. 6.4 应用于随机/控制
    5. 6.5 本章小结
  • 第7章 时滞非线性随机系统Nash微分博弈
    1. 7.1 引言
    2. 7.2 问题描述
    3. 7.3 Nash均衡策略
    4. 7.4 数值算例
    5. 7.5 本章小结
  • 第8章 时滞非线性随机系统的/控制:无限时间情形
    1. 8.1 引言
    2. 8.2 问题描述
    3. 8.3 随机/控制
    4. 8.4 基于T-S模糊模型的随机/控制
    5. 8.5 数值算例
    6. 8.6 本章小结
  • 第9章 时滞随机系统微分博弈在数理金融中的应用
    1. 9.1 引言
    2. 9.2 投资组合选择的博弈分析
    3. 9.3 生产和消费选择的博弈分析
    4. 9.4 本章小结
  • 结论与展望
  • 致谢
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