The Characterization of Clearing Payments in Financial Networks

Clearing payments are payments between agents to settle their mutual liabilities. The interdependence between agents in financial networks complicates the analysis of clearing payments as the extent to which an agent can pay its creditors depends not only on its own assets but also on the incoming payments from the other agents. Each financial network is endowed with agent-specific claims rules that prescribe how each agent pays its creditors. Consequently, our model not only captures standard principles of bankruptcy law, such as limited liability of equity, absolute priority of debt over equity, proportionality, and priority, but also allows for more general underlying payment mechanisms. A payment matrix that contains clearing payments in accordance with claims rules is a transfer scheme, which is not necessarily uniquely determined. This article is the first to provide the complete characterization of all such transfer schemes. Our characterization relies on additional cash vectors, which summarize the payments in excess of the minimum clearing payments. The set of such vectors is shown to be homeomorphic to the set of transfer schemes. We introduce a recursive procedure to compute any additional cash vector, and thereby indirectly a corresponding transfer scheme. The characterization opens up the opportunity for a network-based axiomatic analysis of transfer rules, which prescribe clearing payments for each financial network. In fact, we show that the characterization can be used to provide new axiomatizations of transfer rules in which each agent pays its creditors in accordance with the proportional claims rule.