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
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.
systemic risk; financial networks; clearing; Knaster–Tarski theorem; Eisenberg–Noe model; debt seniority; price impact.
|Russian Science Foundation
|The research of Yuri Kabanov was done under partial financial support of the grant of the Russian Science Foundation No. 14-49-00079.
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Kh. El Bitar, Yu. Kabanov, R. Mokbel, “On uniqueness of clearing vectors reducing the systemic risk”, Inform. Primen., 11:1 (2017), 109–118
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\by Kh.~El Bitar, Yu.~Kabanov, R.~Mokbel
\paper On uniqueness of clearing vectors reducing the systemic risk
\jour Inform. Primen.
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This publication is cited in the following articles:
Yu. M. Kabanov, R. Mokbel, Kh. El Bitar, “Clearing in financial nteworks”, Theory Probab. Appl., 62:2 (2018), 252–277
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