Clearing in financial nteworks
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 311-344 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper is a survey of recent results on the clearing in financial systems. Mathematically, the principal questions of the reviewed studies are on the existence and uniqueness of solutions of specific nonlinear equations $x=f(x)$, where $f:{R}^d\to{R}^d$ is a mapping defined via stochastic and substochastic matrices. Some algorithms of calculations of fixed points are discussed.
Keywords: systemic risk, financial networks, clearing, Knaster–Tarski theorem.
@article{TVP_2017_62_2_a4,
     author = {Yu. M. Kabanov and R. Mokbel and Kh. El Bitar},
     title = {Clearing in financial nteworks},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {311--344},
     year = {2017},
     volume = {62},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a4/}
}
TY  - JOUR
AU  - Yu. M. Kabanov
AU  - R. Mokbel
AU  - Kh. El Bitar
TI  - Clearing in financial nteworks
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2017
SP  - 311
EP  - 344
VL  - 62
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a4/
LA  - ru
ID  - TVP_2017_62_2_a4
ER  - 
%0 Journal Article
%A Yu. M. Kabanov
%A R. Mokbel
%A Kh. El Bitar
%T Clearing in financial nteworks
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2017
%P 311-344
%V 62
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a4/
%G ru
%F TVP_2017_62_2_a4
Yu. M. Kabanov; R. Mokbel; Kh. El Bitar. Clearing in financial nteworks. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 311-344. http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a4/

[1] D. Acemoglu, A. Ozdaglar, A. Tahbaz-Salehi, “Systemic risk and stability in financial networks”, Amer. Economic Rev., 105:2 (2015), 564–608; NBER Working Paper Series, 2013, 18727, 45 pp. | DOI

[2] H. Amini, D. Filipović, A. Minca, “To fully net or not to net: adverse effects of partial multilateral netting”, Oper. Res., 64:5 (2016), 1135–1142 ; Swiss Finance Institute Research Paper Series, 2014, 14-63, 22 pp. | DOI | MR | Zbl | DOI

[3] R. Cifuentes, G. Ferrucci, Hyun Song Shin, “Liquidity risk and contagion”, J. Eur. Econ. Assoc., 3:2-3 (2005), 556–566 | DOI

[4] R. Cont, L. Wagalath, “Fire sale forensics: measuring endogenous risk”, Math. Finance, 26:4 (2015), 835–866 | DOI | MR | Zbl

[5] L. Eisenberg, T. H. Noe, “Systemic risk in financial systems”, Manag. Sci., 47:2 (2001), 236–249 | DOI | Zbl

[6] K. El Bitar, Yu. Kabanov, R. Mokbel, “On uniqueness of clearing vectors reducing the systemic risk”, Inform. i ee primen., 11:1 (2017), 109–118 | DOI

[7] H. Elsinger, “Financial networks, cross holdings, and limited liability”, Oesterreichische Nationalbank Working Papers, 2009, 156, 37 pp.

[8] Z. Feinstein, “Financial contagion and asset liquidation strategies”, Oper. Res. Lett., 45:2 (2017), 109–114 | DOI | MR

[9] T. Fischer, “No-arbitrage pricing under systemic risk: accounting for cross-ownership”, Math. Finance, 24:1 (2014), 97–124 | DOI | MR | Zbl

[10] R. A. Horn, C. R. Johnson, Matrix analysis, Cambridge Univ. Press, Cambridge, 1985, xiii+561 pp. | DOI | MR | MR | Zbl | Zbl

[11] P. Milgrom, J. Roberts, “Comparing equilibria”, Amer. Econ. Rev., 84:3 (1994), 441–454

[12] E. Presman, “A new approach to the solution of optimal stopping problem in a discrete time”, Stochastics, 83:4-6 (2011), 467–475 | DOI | MR | Zbl

[13] L. C. G. Rogers, L. A. M. Veraart, “Failure and rescue in an interbank network”, Manag. Sci., 59:4 (2013), 882–898 | DOI

[14] A. N. Shiryaev, Optimal stopping rules, Appl. Math., 8, Springer-Verlag, New York–Heidelberg, 1978, x+217 pp. | MR | MR | Zbl | Zbl

[15] I. M. Sonin, “The optimal stopping of a Markov chain and recursive solution of Poisson and Bellman equations”, From stochastic calculus to mathematical finance, The Shiryaev festschrift, Springer, Berlin, 2006, 609–621 | DOI | MR | Zbl

[16] T. Suzuki, “Valuing corporate debt: the effect of cross-holdings of stock and debt”, J. Oper. Res. Soc. Japan, 45:2 (2002), 123–144 | MR | Zbl

[17] A. Tarski, “A lattice-theoretical fixpoint theorem and its applications”, Pacific J. Math., 5:2 (1955), 285–309 | DOI | MR | Zbl