A distributed algorithm for systemic risk mitigation in financial systems

This paper studies the problem of optimally allocating a cash injection into a financial system in distress. We investigate a one-period borrower-lender network with no dynamics, in which all debts are due at the same time and have the same seniority. Every node in the network represents a financial institution, and every node is labeled with a nonnegative real number which is the cash on hand that the institution has before the debts are due. If node i owes d dollars to node j, this is represented in the network as a directed edge from node i to node j with weight d. We propose a duality-based distributed algorithm to determine the optimal cash injection amount C and its corresponding optimal allocation among the nodes, to minimize the cost function C+λD which is a linear combination of two terms: the total cash injected into the system and the total unpaid liabilities D in the system after the cash injection. The user-selected coefficient λ controls the relative importance of the two terms in the cost function.