On the Unification of Centralized and Decentralized Clearing Mechanisms in Financial Networks

We analyze clearing mechanisms in financial networks in which agents may have both monetary individual assets and mutual liabilities. A clearing mechanism prescribes mutual payments between agents to settle their mutual liabilities. The corresponding payments, summarized in a payment matrix, are made in accordance with agent specific claims rules that stem from the vast literature on claims problems. We show that large classes of centralized and decentralized clearing mechanisms all prescribe the same payment matrix under the condition that the underlying claims rules satisfy composition; a property satisfied by the proportional rule that is often applied in insolvency proceedings. This payment matrix is the one that contains the minimal amount of payments required to clear the network. In fact, we show that composition guarantees unification of clearing mechanisms in which agents pay simultaneously and clearing mechanisms in which agents pay sequentially in any arbitrary order. Therefore, for a given financial network, each clearing mechanism gives rise to the same transfer allocation. Moreover, we provide an axiomatic characterization of the corresponding mutual claims rule on the basis of five axioms: scale invariance, equal treatment of equals, composition, path independence and consistency. This characterization extends the analogous characterization for claims rules as given by Moulin (2000).