Optimal Clearing Payments in a Financial Contagion Model

Financial networks are characterized by complex structures of mutual obligations. These obligations are fulfilled entirely or in part (when defaults occur) via a mechanism called clearing, which determines a set of payments that settle the claims by respecting rules such as limited liability, absolute priority, and proportionality (pro-rated payments). In the presence of shocks on the financial system, however, the clearing mechanism may lead to cascaded defaults and eventually to financial disaster. In this paper, we first study the clearing model under pro-rated payments of Eisenberg and Noe, and we derive novel necessary and sufficient conditions for the uniqueness of the clearing payments, valid for an arbitrary topology of the financial network. Next, we observe that the proportionality rule is a factor that potentially concurs to the cascaded defaults effect, and that the aggregated systemic loss can be reduced if this rule is lifted. We thus shift the focus from the individual interest to the overall systemic interest to contain the adverse effects of cascaded failures, and we show that pro-rate-free clearing payments can be computed uniquely by solving suitable convex optimization problems.