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

Abstract

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 agentspecific 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).

Centralized Clearing Mechanisms in Financial Networks: A Programming Approach

“…The set of solutions to this system forms a complete lattice, which implies that there is a least and a greatest clearing payment matrix. Csóka and Herings (2018) show in a decentralized set-up that a large class of decentralized clearing processes converges to the least clearing payment matrix and Ketelaars and Borm (2021) derive an analogous result in a continuous set-up. In this paper, we therefore examine how a centralized approach can be used to select the greatest clearing payment matrix.…”

“…4 Centralized Clearing as a Programming Problem Csóka and Herings (2018) show in a discrete set-up that decentralized clearing results in the least clearing payment matrix. Ketelaars and Borm (2021) consider the continuous setup and show that decentralized clearing processes converge to the least clearing payment matrix under mild conditions. Consider a decentralized clearing process where all agents simultaneously make the largest payments that are compatible with their cash at hand.…”

Duality in Financial Networks

“…Alternatively, Groote Schaarsberg, Reijnierse, and Borm (2018) uses a constructive proof to show existence of ϕ-transfer schemes when all agents use the same arbitrary claims rule and estates are non-negative. Ketelaars and Borm (2021) extends this constructive proof to arbitrary agent-specific claims rules and explicitly characterize the bottom ϕ-transfer scheme. Moreover, Csóka and Herings (2018) shows Proposition 3.4 for a discrete setup, but not allowing for negative estates.…”

“…We follow the convention that bankruptcy rules dictate the payments between the agents in the financial network, although we allow for general agent-specific bankruptcy rules (cf. Csóka and Herings (2018); Ketelaars and Borm (2021); Csóka and Herings (2023)).…”

“…More specifically, let (E, C) ∈ L N , let ϕ be a vector of claims rules, and, for all k ∈ N, define P k+1 = f ϕ (P k ; E, C). Ketelaars and Borm (2021) shows that, in the case all estates are non-negative, the bottom ϕ-transfer scheme is the limit of the sequence (P k ) k∈N with starting point P 1 = 0 N ×N . In the following theorem, we generalize this result by allowing for negative estates.…”