Systematic Risk And Nash Equilibrium Of An Inter-bank Borrowing And Lending System

Systemic risk has attracted more and more attention in the financial market.As a reading note,this paper refers to the article of Carmona,Fouque and Sun and some ref-erences mentioned in the article.In this paper,we make minor change to the inter-bank borrowing and lending system model in[3].The system is described as a stochas-tic differential dynamic system with inhomogeneous diffusion coefficient coupled by mean field and common noise.The model in[3]is described as homogeneous coupled diffusion system.At first,We describe the stability of the system under this model by numerical simulation,and reveal the importance of risk preference management in the financial system by comparing the default degree of the system under different risk pref-erence levels.Then we define "systemic risk" with mathematical language and give an analytical expression.Next,based on the model,we introduce a multi-agents game.In this game,the control strategy of each bank is the interest rate they borrowing from or leading to the central bank,and the goal of each bank is to minimize its own objective function.There is a Nash equilibrium in this game.We give the Nash equilibrium under the open-loop control strategy and the closed-loop control strategy respectively.