An Axiomatization of the Proportional Rule in Financial Networks

Csóka, Péter; Herings, P. Jean-Jacques

doi:10.1287/mnsc.2020.3700

Cited by 18 publications

(26 citation statements)

References 39 publications

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“…By Theorem 7.2, these bankruptcy rules are continuous. Such a result was also obtained in Csóka and Herings (2017) for the special case where all initial endowments are strictly positive. They also present the following example to show that a similar result does not hold for the constrained equal awards bankruptcy rule.…”

Section: Bankruptcy Rulessupporting

confidence: 59%

“…The literature has found a number of conditions to obtain a unique clearing payment matrix. In this section, we show how earlier findings by Eisenberg and Noe (2001), Glasserman and Young (2015), Csóka and Herings (2017), Groote Schaarsberg, Reijnierse, and Borm (2018), and Koster (2019) are special cases of the condition presented in Theorem 4.5.…”

Section: Relation To Other Uniqueness Conditions In the Literaturementioning

confidence: 67%

“…As we noted before, the constrained equal losses division rule does not satisfy strict monotonicity. Our generalization to positive monotonicity in Theorem 4.5 guarantees that the clearing payment matrix is unique when all agents use the constrained equal losses division rule and endowments of cyclical agents are all positive, a result that was also stated as Theorem 7.8 in Csóka and Herings (2017). This result is in stark contrast with the case of constrained equal awards division rules as will be demonstrated in Example 6.1 of Section 6.…”

Section: Then Feasibility and Priority Of Creditors Imply That Ementioning

confidence: 84%

“…Continuity is an attractive property of a bankruptcy rule since it implies that small changes in the financial network induce small changes in the resulting payment matrix. Continuity is also used as an axiom in Csóka and Herings (2021) in order to axiomatize the proportional bankruptcy rule. The next result states that b is continuous at any financial network with a unique clearing payment matrix.…”

Section: Bankruptcy Rulesmentioning

confidence: 99%

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Uniqueness of Clearing Payment Matrices in Financial Networks

Csóka

Herings

2024

Mathematics of OR

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We study bankruptcy problems in financial networks in the presence of general bankruptcy laws. The set of clearing payment matrices is shown to be a lattice, which guarantees the existence of a greatest clearing payment and a least clearing payment. Multiplicity of clearing payment matrices is both a theoretical and a practical concern. We present a new condition for uniqueness that generalizes all the existing conditions proposed in the literature. Our condition depends on the decomposition of the financial network into strongly connected components. A strongly connected component that contains more than one agent is called a cycle, and the involved agents are called cyclical agents. If there is a cycle without successors, then one of the agents in such a cycle should have a strictly positive endowment. The division rule used by a cyclical agent with a strictly positive endowment should be positive monotonic, and the rule used by a cyclical agent with a zero endowment should be strictly monotonic. Because division rules involving priorities are not positive monotonic, uniqueness of the clearing payment matrix is a much bigger concern for such division rules than for proportional ones. As a final contribution of the paper, we exhibit the relationship between the uniqueness of clearing payment matrices and the continuity of bankruptcy rules, a property that is very much desired for stability of financial systems. Funding: This research was supported by the Higher Education Institutional Excellence Program 2020 of the Ministry of Innovation and Technology in the framework of the “Financial and Public Services” research project [Grant TKP2020-IKA-02] at Corvinus University of Budapest. P. Csóka received funding from the National Research, Development and Innovation Office [Grants K-120035 and K-138826].

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Section: Bankruptcy Rulessupporting

confidence: 59%

Section: Relation To Other Uniqueness Conditions In the Literaturementioning

confidence: 67%

Section: Then Feasibility and Priority Of Creditors Imply That Ementioning

confidence: 84%

Section: Bankruptcy Rulesmentioning

confidence: 99%

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Uniqueness of Clearing Payment Matrices in Financial Networks

Csóka

Herings

2024

Mathematics of OR

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“…In this characterization, φ is the Talmud rule (Aumann & Maschler, 1985). Second, Csóka and Herings (2021) provide an axiomatic characterization of the proportional rule in financial networks.…”

Section: Introductionmentioning

confidence: 99%

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

Ketelaars

Borm

2021

SSRN Journal

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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).

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Broadcasting revenue sharing after cancelling sports competitions

Bergantiños

Moreno‐Ternero

2023

Ann Oper Res

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The COVID-19 pandemic forced the partial or total cancellation of most sports competitions worldwide. Sports organizations crucially rely on revenues raised from broadcasting. How should the allocation of these revenues be modified when sports leagues are cancelled? We aim to answer that question in this paper by means of the axiomatic approach. Two extension operators (dubbed zero and leg operators, respectively) will play a major role in our analysis. We show that several combinations of axioms (formalizing ethical or strategic principles) characterize the image via those operators of two focal rules: the equal-split rule and concede-and-divide.

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An Axiomatization of the Proportional Rule in Financial Networks

Cited by 18 publications

References 39 publications

Uniqueness of Clearing Payment Matrices in Financial Networks

Uniqueness of Clearing Payment Matrices in Financial Networks

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

Broadcasting revenue sharing after cancelling sports competitions

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