银行货币储备博弈的强化学习方法  

REINFORCEMENT LEARNING METHODS FOR BANK CURRENCY RESERVE GAMES

作　　者：李策 LI Ce(School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学数学科学学院,安徽合肥230026

出　　处：《数学杂志》2025年第1期81-94,共14页Journal of Mathematics

摘　　要：在大规模银行交互系统中,各银行可通过控制与中央银行的借贷率来使自身对数货币储备尽可能地接近样本均值,从而降低系统性风险发生的概率.然而当状态过程与目标函数的参数未知时,无法直接求解随机微分博弈问题得到纳什均衡.本文结合平均场博弈理论与连续时间强化学习的相关方法,构造了一组大规模银行借贷网络中的近似纳什均衡.首先通过求解向前向后耦合HJB-FPK方程,得到代表银行的平均场均衡策略;再通过所得策略的形式,设计出迭代参数的方法用以刻画参数未知时的近似最优策略;最后通过学到的参数,构造银行数量较大时的近似纳什均衡.borrowing and lending rates with the central bank to bring their currency reserves as close as possible to the sample mean,thereby reducing the probability of systemic risk.However,when the state process and parameters of the objective function are unknown,it is not directly possible to solve the stochastic differential game problem to obtain a Nash equilibrium.In this study,we combined mean-field game theory with relevant methods from continuous-time reinforcement learning to construct an approximate Nash equilibrium in a large-scale bank lending network.First,by solving the forward-backward coupled HJB-FPK equation,we obtained the mean-field equilibrium strategy representing the banks.Next,based on the form of the obtained strategy,we designed an iterative parameter method to characterize the approximate optimal strategy when parameters are unknown.Finally,using the learned parameters,we constructed an approximate Nash equilibrium for a large number of banks.

关 键 词：系统性风险 强化学习 近似纳什均衡 平均场博弈 

分 类 号：O211.9[理学—概率论与数理统计]