基于分数布朗运动驱动的银行货币存贮网络模型系统风险和最优控制的研究

从银行间货币流动的动力学角度出发,提出了一个由分数布朗运动驱动的并且有中央银行参与的银行货币存储网络模型.每家银行以特定的比率从其他银行拆借货币,并在一定的情况下可以向中央银行拆借资金,但由此会产生借贷成本.系统中银行的货币存储满足文中给出的随机微分方程,计算并给出了系统风险指标--总体破产概率,系统活动总量的数学表达式,通过线性二次型控制方法,求得银行向中央银行拆借资金的最优成本.

Study on the systemic risk and optimal control of bank money storage network model based on fractional Brownian motion

Based on the dynamics of inter-bank money flow, a bank money storage network model driven by fractional Brownian motion and involving central bank is proposed. Each bank borrows money from other banks at a specific rate and, in certain circumstances, can borrow money from the central bank, but that creates borrowing costs. The money store of the bank in the system satisfies the stochastic differential equation given in the paper. The mathematical expression of system risk index-the overall probability of bankruptcy and total system activity is given, the optimal cost of borrowing funds from the central bank is obtained by linear quadratic control method.