Systemic Risk Analysis In Financial Scenario With Bipartite Graph Structure

In this paper,we study the effect of network structure between agents and objects on measures for systemic risk in the financial field.We model the relationship between agents and objects by a bipartite graph.In order to better describe the risk distribution of objects,a priori structure is added in this paper,thus,the risk of objects is subordinated to the multivariate Pareto distribution of the second kind.In addition,we extend the multivariate Pareto distribution of the second kind to a more generalized multivariate distribution whose form is P(X1>x1,..…,Xn>xn)= h(?i=1 n?ixi),where the sur-vival function h is a multivariate function of order(n-1)such that h(0)= 1,?i>0 for all i and ?i??j for all i?j.Since the tail conditional expectation(TCE)which de-scribes the expected amount of risk that can be experienced given that the risk exceeds a threshold value provides an important measure of the right-tail risk in risk analysis,we can choose the tail conditional expectations as the conditional risk measurement of agents.We find out that the tool of divided difference is very convenient for the eval-uation of tail risk measures when the risk of objects is subordinated to the generalized distribution we mentioned above.In terms of divided differences,we will calculate the tail conditional expectations mentioned above.Furthermore,we will introduce an-other method to calculate the outcomes of the n-variate case recursively in terms of the(n-1)-variate case in case of the multivariate Pareto distribution of the second kind.Finally,We provide numerical examples to illustrate the method.