Diffusion on Dynamical Interbank Loan Networks

In this paper we study the effect of diffusion method to interbank networks in concept of connected, directed and weighted networks. We consider networks of n different banks which they exchange funds (loans) and the main feature is how the leverages of banks can be choosen to improve the financial stability of the network. This is done by considering differential equations of diffusion type. It is well known that banks exchange funds in the form of credit which are supported partly by the banks own capital. The ratio of their assets by the capital constitute the leverage of the bank and for minimization of risk purposes this ratio has to be kept within reasonable limits. The aim of this paper is to show how ideas from diverse domains such as diffusion, differential equations and graph theory can be used to demonstrate how financial risk can be controlled in this type of interbank networks. Diffusion acts as a stabilization process by the flow of funds from banks of higher leverage to those of lower. This process leads to equilibrium and stops either in a state of equal leverages between banks or whenever this is not possible in a final state which is more robust compared to the initial. The relation between the initial and final values of the interbank network may be described by a projection operator.