A Note on Uniqueness of Clearing Prices in Financial Systems

Koster, Maurice

doi:10.2139/ssrn.3427039

Cited by 3 publications

(8 citation statements)

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“…Eisenberg and Noe (2001) assume proportional division rules and require the financial network to be regular: every agent has at least one successor with a positive endowment. Koster (2019) generalizes this finding and shows that regularity is a sufficient condition for uniqueness of the clearing payment matrix when all agents use strictly monotonic division rules. Regularity implies that in every cycle without successors there is at least one agent with a positive endowment.…”

Section: Introductionsupporting

confidence: 64%

“…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, andBorm (2018), andKoster (2019) are special cases of the condition presented in Theorem 4.5.…”

Section: Relation To Other Uniqueness Conditions In the Literaturementioning

confidence: 75%

“…Proposition 5.4 (Koster (2019)). Let N = (I, z, L, d) be a regular financial network such that all agents use a strictly monotonic division rule.…”

Section: Relation To Other Uniqueness Conditions In the Literaturementioning

confidence: 93%

“…The proposition also applies to division rules which are not proportional. Koster (2019) extends the regularity condition of Eisenberg and Noe (2001) from proportional division rules to strictly monotonic division rules.…”

Section: Relation To Other Uniqueness Conditions In the Literaturementioning

confidence: 99%

“…The system of equations we use to characterize clearing payment matrices is slightly different from the one used in Eisenberg and Noe (2001) for proportional division rules and the one in Koster (2019) for general division rules. In those two papers, each |I|dimensional row of the payment matrix is represented by a one-dimensional parameter, like the fraction of total liabilities that are paid in Eisenberg and Noe (2001).…”

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confidence: 99%

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Uniqueness of Clearing Payment Matrices in Financial Networks

Csóka

Herings

2021

SSRN Journal

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Section: Introductionsupporting

confidence: 64%

Section: Relation To Other Uniqueness Conditions In the Literaturementioning

confidence: 75%

“…Proposition 5.4 (Koster (2019)). Let N = (I, z, L, d) be a regular financial network such that all agents use a strictly monotonic division rule.…”

Section: Relation To Other Uniqueness Conditions In the Literaturementioning

confidence: 93%

Section: Relation To Other Uniqueness Conditions In the Literaturementioning

confidence: 99%

mentioning

confidence: 99%

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Uniqueness of Clearing Payment Matrices in Financial Networks

Csóka

Herings

2021

SSRN Journal

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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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An Axiomatization of the Pairwise Netting Proportional Rule in Financial Networks

Csóka,

Herings

2024

SSRN Journal

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A Note on Uniqueness of Clearing Prices in Financial Systems

Cited by 3 publications

References 16 publications

Uniqueness of Clearing Payment Matrices in Financial Networks

Uniqueness of Clearing Payment Matrices in Financial Networks

Uniqueness of Clearing Payment Matrices in Financial Networks

An Axiomatization of the Pairwise Netting Proportional Rule in Financial Networks

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