Research On The Measurement Index Of Systemic Risk In Financial Networks

In 2008,the "subprime crisis" broke out in the United States,which caused a large number of financial institutions around the world to suffer serious impact.Some financial institutions went bankrupt or were on the verge of bankruptcy,thus triggering a severe financial crisis that affected the world economy.This crisis has made more and more people realize that although the network structure can play a very important role in resisting financial risks on the one hand,on the other hand,it may lead to the contagion of shocks in the networks and thus form the systemic risk.As an important part of the traditional financial industry "troika",banking industry is in a very important core position in a country's social production and life,and is also related to the general public.The inter-bank loan market has become the main source of financing for Banks to solve the temporary shortage of funds.With the continuous development of the banking industry,a very complex financial network structure of risk sharing has been formed among Banks.It is an important task to evaluate the systemic risk of the network,which is of great significance to maintain the stability of the financial system.Basing on the existing research,based on the stochastic differential system,this paper attempts to establish two different models to measure the system risk of inter-bank network under the new system environment of Fractional Brownian Motion,based on the dynamics of inter-bank money flow.Combined with the model,the systematic risk of inter-bank network is studied by means of systematic risk metrics such as average default distance,overall bankruptcy probability and systematic activity.Firstly,a bank money lending network model considering external shocks is established,in which each bank borrows money from other banks in the system at a specific ratio,and the compound Poisson process is used to describe the sudden external shocks to the system at a certain moment,thus affecting the currency storage level of each bank.Among them,the currency storage of each banks in the system satisfies the stochastic,differential equation w:ith jump driven by fractional Brownian motion,and proves the existence and uniqueness of the solution of the equation,and gives the mathematical expression of the system risk metric--average default distance(ADD)through calculation.The important parameters in the expression are simulated numerically.Then,a new network model of inter-bank money lending is established with the participation of the central bank.The mathematical expression of the overall bankruptcy probability,which is a measure of systemic risk,is obta:ined through calculation.In addition,the mathematical expression of the total amount of inter-bank activity of the model is given through calculation and analyzed with practice.Finally,according to the model,the optimal cost of borrowing money from the central bank is calculated by linear quadratic control method.The structure of the article is as follows:In chapter one,this paper mainly introduces the purpose and theoretical significance of the topic selection,the existing research results of other scholars in this field,and the framework structure of the paper.In chapter two,this paper mainly introduces the model basis,the basic theoretical knowledge and methods involved in this paper.In chapter three,based on random analysis of fractional Brownian motion driven stochastic differential equations with jump,it is proved that the model has a unique non-negative strong solution.In addition,the mathematical expression of average default distance is calculated.And the important parameters in the expression are simulated and analyzed in combination with practice.In chapter four,a bank's money lending network model with the participation of the central bank is established.The overall bankruptcy probability of the bank network is calculated.According to the mathematical expression of the overall bankruptcy probability,numerical simulation is carried out,and the simulation results are analyzed in combination with the actual situation.In addition,the mathematical expression of the total amount of inter-bank activity of the model is given through calculation and analyzed in combination with the actual situation.Finally,the optimal cost of borrowing money from the central bank is calculated by the stochastic linear quadratic control method.Chapter five summarizes the main research contents of this paper and prospects the future research direction.