An Iterative Approach to Reduce Systemic Risk among Financial Institutes

Abstract

Financial institutions are interconnected by holding debt claims against each other. The interconnection is a key contributing factor to the past worldwide financial crisis. A default bank may cause its creditors to default, and the risk may be further propagated to up-stream institutes. We study how the mechanism of default liquidation affects the total wealth of the financial system and curbs the risk contagion. We formulate this problem as a nonlinear optimization problem with equilibrium constraints and propose an optimal liquidation policy to minimize the system’s loss without changing the partition of default and non-default banks. We show that the optimization problem resembles a Markov decision problem (MDP) and therefore we can apply the direct-comparison based optimization approach to solve this problem. We derive an iteration algorithm which combines both the policy iteration and the gradient based approach. Our work provides a new direction in curbing the risk contagion in financial networks; and it illustrates the advantages of the direct-comparison based approach, which originated in the field of discrete event dynamic system, in nonlinear optimization problems.