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Inform. Primen., 2017, Volume 11, Issue 1, Pages 109–118 (Mi ia464)  

This article is cited in 1 scientific paper (total in 1 paper)

On uniqueness of clearing vectors reducing the systemic risk

Kh. El Bitara, Yu. Kabanovabc, R. Mokbela

a Laboratoire de Mathématiques, Université de Franche-Comté, 16 Route de Gray, 25030 Besançon, CEDEX, France
b Institute of Informatics Problems, Federal Research Center Computer Science and Control of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
c National Research University MPEI, 14 Krasnokazarmennaya Str., Moscow, 111250, Russian Federation

Abstract: Clearing of financial system, i. e., of a network of interconnecting banks, is a procedure of simultaneous repaying debts to reduce their total volume. The vector whose components are repayments of each bank is called clearing vector. In simple models considered by Eisenberg and Noe (2001) and, independently, by Suzuki (2002), it was shown that the clearing to the minimal value of debts accordingly to natural rules can be formulated as fixpoint problems. The existence of their solutions, i. e., of clearing vectors, is rather straightforward and can be obtained by a direct reference to the Knaster–Tarski or Brouwer theorems. The uniqueness of clearing vectors is a more delicate problem which was solved by Eisenberg and Noe using a graph structure of the financial network. The uniqueness results have been proved in two generalizations of the Eisenberg–Noe model: in the Elsinger model with seniority of liabilities and in the Amini–Filipovic–Minca type model with several types of illiquid assets whose firing sale has a market impact.

Keywords: systemic risk; financial networks; clearing; Knaster–Tarski theorem; Eisenberg–Noe model; debt seniority; price impact.

Funding Agency Grant Number
Russian Science Foundation 14-49-00079
The research of Yuri Kabanov was done under partial financial support of the grant of the Russian Science Foundation No. 14-49-00079.


DOI: https://doi.org/10.14357/1992264170110

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Received: 25.09.2016
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Citation: Kh. El Bitar, Yu. Kabanov, R. Mokbel, “On uniqueness of clearing vectors reducing the systemic risk”, Inform. Primen., 11:1 (2017), 109–118

Citation in format AMSBIB
\Bibitem{El KabMok17}
\by Kh.~El Bitar, Yu.~Kabanov, R.~Mokbel
\paper On uniqueness of clearing vectors reducing the systemic risk
\jour Inform. Primen.
\yr 2017
\vol 11
\issue 1
\pages 109--118
\mathnet{http://mi.mathnet.ru/ia464}
\crossref{https://doi.org/10.14357/1992264170110}
\elib{http://elibrary.ru/item.asp?id=29159460}


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    This publication is cited in the following articles:
    1. Yu. M. Kabanov, R. Mokbel, Kh. El Bitar, “Clearing in financial nteworks”, Theory Probab. Appl., 62:2 (2018), 252–277  mathnet  crossref  crossref  mathscinet  isi  elib
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