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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (3): 551-567.doi: 10.3969/j.issn.1005-3085.2024.03.013

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部分信息下带时滞的鲁棒资产负债博弈问题研究

杨  璐1,  张成科2,  朱怀念2,  徐  萌3   

  1. 1. 广东技术师范大学管理学院，广州 510450
    2. 广东工业大学经济学院，广州 510520
    3. 广东工业大学管理学院，广州 510520
  • 收稿日期:2021-11-08 接受日期:2022-12-25 出版日期:2024-06-15 发布日期:2024-08-15
  • 基金资助:
    国家社会科学基金(21FJYB025)；广州市哲学社科规划(2023GZGJ15).

Robust Asset-liability Investment Game with Time Delay under Partial Information

YANG Lu1,  ZHANG Chengke2,  ZHU Huainian2,  XU Meng3   

  1. 1. School of Management, Guangdong Polytechnic Normal University, Guangzhou 510450
    2. School of Economics, Guangdong University of Technology, Guangzhou 510520
    3. School of Management, Guangdong University of Technology, Guangzhou 510520
  • Received:2021-11-08 Accepted:2022-12-25 Online:2024-06-15 Published:2024-08-15
  • Supported by:
    The National Social Science Foundation of China (21FJYB025); the Philosophy and Social Science Project of Guangzhou City (2023GZGJ15).

摘要： 研究了部分可观测信息下带时滞的鲁棒资产负债博弈问题，运用滤波理论，将不完全信息转化为完全信息，以终端相对财富的效用最大化为目标，构建了不完全信息带时滞的鲁棒资产负债博弈问题，借助动态规划原理，得到了均衡投资策略和值函数的显示表达式。最后，通过数值模拟验证了参数对均衡投资策略和值函数的影响，主要得出了不完全信息下投资者的效用低于完全信息。所以，投资者应尽可能的搜集与投资相关的更多信息，以便于做出更加明智的决策。

关键词: 鲁棒均衡策略, 滤波理论, 时滞, 效用最大化, 部分信息

Abstract: This paper discusses the robust asset-liability management problem of maximizing the expected utility of the terminal wealth under partial information with delay, that is, the investors can observe the risky asset price with random drift which is not directly observable in the financial market. It is reduced to a partially observed stochastic differential game problem. This paper tries to an effort to find the equilibrium strategies by maximizing the expected utility of the insurer's terminal wealth with delay under the worst-case scenario of the alternative measures. By using the idea of filtering theory and the dynamic programming approach, we derive the robust equilibrium strategies and value functions explicitly. Finally, some numerical examples are presented. Obviously, the value function is higher in the full information case than it in the partial information case. Therefore, investors should collect more information related to investment as much as possible in order to make more informed decisions.

Key words: robust equilibrium strategies, filtering theory, delay, utility maximization, partial information

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