On the resolution of cross-liabilities

In a variety of situations, entities in a system, for example firms in the financial sector, hold liabilities on each other. The reimbursement abilities are intertwined, thereby potentially generating coordination failures and a cascade of defaults calling for interventions. Interventions can be discretionary or designed by rules such as bankruptcy laws. Bankruptcy laws, however, manage the default of a single firm towards its creditors, without considering all those that could be affected indirectly by the resolution. To account for these indirect effects, resolution rules should be defined at the system level. This paper investigates such rules, assuming that the primary goal of the resolution is to avoid defaults on external debts, say, banks' defaults on deposits. Focusing on the proportionality principle, it defines and characterizes the constrained-proportional rule, building on two approaches: the minimization of an inequality measure of the reimbursements (made and received) and the axiomatization through desirable properties.