The recent economic crisis has raised a wide awareness that the financial system should be considered as a complex network with financial institutions and financial dependencies respectively as nodes and links between these nodes. Systemic risk is defined as the risk of default of a large portion of financial exposures among institution in the network. Indeed, the structure of this network is an important element to measure systemic risk and there is no widely accepted methodology to determine the systemically important nodes in a large financial network. In this research, we introduce a metric for systemic risk measurement with taking into account both common idiosyncratic shocks as well as contagion through counterparty exposures. Our focus is on application of eigenvalue problems, as a robust approach to the ranking techniques, to measure systemic risk. Recently, the efficient algorithm has been developed for robust eigenvector problem to reduce to a nonsmooth convex optimization problem. We applied this technique and studied the performance and convergence behavior of the algorithm with different structure of the financial network.
