最优投资与风险控制策略的多人非零和博弈及平均场博弈

doi:10.12052/gdutxb.220124

摘要/Abstract

摘要： 金融市场中存在大量的机构投资者，机构投资者追求高回报高财富的特性导致市场竞争日益激烈，竞争的市场环境使得机构投资者不仅追求自身财富的最大化，还关注与竞争对手之间的财富差距。本文研究多个机构投资者策略互动下的投资与风险控制问题。假设每个投资者均可以将财富投资于金融市场中以实现财富增值，同时通过购买保险等方式将面临的风险部分转移给其他金融机构。使用投资者自身财富与市场平均财富之差描述的相对业绩刻画市场竞争，投资者的目标是最大化终端时刻相对绩效的期望效用，在非零和博弈框架下构建了多人投资与风险控制博弈模型，以CARA效用函数为例，运用随机微分博弈理论和平均场博弈理论求出Nash均衡状态下的最优投资与风险控制策略，并进行参数的敏感性分析。研究发现：竞争将导致风险投资攀升，风险控制减弱，从而导致金融市场的系统性风险增加；机构投资者自身及竞争对手的风险偏好和市场竞争程度均会影响均衡投资与风险控制策略；盈余波动影响风险控制策略发生同向改变，但这种影响在波动轻微时较为明显，当波动超过一定程度时，波动对风险控制策略影响甚微。研究为机构投资者的投资与风险控制策略选择提供了有益指导。

关键词: 投资与风险控制, 非零和博弈, 平均场博弈, Nash均衡, 动态规划

Abstract: There are a large number of institutional investors in the financial market. The characteristics of institutional investors pursuing high returns and high wealth lead to increasingly fierce market competition. The competitive market environment makes institutional investors not only pursue the maximization of their own wealth, but also pay attention to the wealth gap between them and their competitors. The investment and risk control problem under the interaction of multiple institutional investors' strategies was studied, considering the situation that there are a large number of institutional investors in the market. It is assumed that each investor can invest his wealth in the financial market to realize wealth appreciation, and at the same time transfer the risks he faces to other financial institutions in the market by purchasing insurance and other means. The relative performance described by the difference between the investor's own wealth and the market average wealth is used to describe the market competition. The objective of the investor is to maximize the expected utility of the relative performance at the terminal moment. A multi person investment and risk control game model is constructed under the non-zero sum game framework. Taking the CARA utility function as an example, the optimal investment and risk control strategy under the Nash equilibrium state is obtained by using the stochastic differential game theory and the mean field game theory, and the sensitivity analysis of parameters is carried out. The research finds that: (1) Competition will lead to the rise of venture capital and the weakening of risk control, which will lead to the increase of systemic risk in the financial market; (2) The risk preference and market competition of institutional investors and their competitors will affect the balanced investment and risk control strategy; (3) Earnings fluctuation affects the risk control strategy in the same direction, but this effect is more obvious when the fluctuation is slight. When the fluctuation exceeds a certain degree, the fluctuation has little impact on the risk control strategy. The research provides useful guidance for institutional investors to choose investment and risk control strategies.

Key words: investment and risk control, non-zero-sum game, mean field game, Nash equilibrium, dynamic programming

中图分类号:

F830.59

莫仕茵, 朱怀念. 最优投资与风险控制策略的多人非零和博弈及平均场博弈[J]. 广东工业大学学报, 2023, 40(05): 123-132.

Mo Shi-yin, Zhu Huai-nian. N-agent and Mean Field Game for Optimal Investment and Risk Control Strategies[J]. Journal of Guangdong University of Technology, 2023, 40(05): 123-132.

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