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 in a financial network 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 situations. The bottom payment matrix is the payment matrix that contains the minimal amount of payments required to clear the network. We explicitly characterize the bottom payment matrix as the result of a recursive centralized mechanism. We subsequently show that several types of decentralized clearing mechanisms lead to the bottom payment matrix as well. In fact, we show that this unification of centralized and decentralized clearing mechanisms relies on the composition property of the underlying agent-specific claims rules that dictate the payment mechanism.