Stability in a model of interbank lending

SIAM Journal on Financial Mathematics

Volumn 4, Issue 1, 2013, Pages 784-803

  Fouque, Jean Pierre ^a   Ichiba, Tomoyuki ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Exit system; Feller diffusion; Interacting particle system algorithm; Interbank lending system; Multiple defaults; Stability; Systemic risk

Indexed keywords

EID: 84893536600     PISSN: None     EISSN: 1945497X     Source Type: Journal    
DOI: 10.1137/110841096     Document Type: Article

References (32)

1. D.A. Adams, R.M. Ziff, and L.M. Sander, Computation of nucleation at a nonequilibrium first-order phase transition using a rare-event algorithm, J. Chem. Phys., 133 (2010), 174107.
2. T. Adrian and H.S. Shin, Liquidity and leverage, J. Financ. Intermed., 19 (2010), pp. 418-437.
3. A.D. Banner and R. Ghomrasni, Local times of ranked continuous semimartingales, Stochastic Process. Appl., 118 (2008), pp. 1244-1253.
4. R. F. Bass and E. A. Perkins, Degenerate stochastic differential equations with Holder continuous coefficients and super-Markov chains, Trans. Amer. Math. Soc., 355 (2003), pp. 373-405.
5. R. Carmona, J.-P. Fouque, and L.-H. Sun, Mean field games and systemic risk, Commun. Math. Sci., submitted.
6. R. Carmona, J.-P. Fouque, and D. Vestal, Interacting particle systems for the computation of rare credit portfolio losses, Finance Stoch., 13 (2009), pp. 613-633.
7. R. Cont and J.P. Bouchaud, Herd behavior and aggregate fluctuations in financial markets, Macroecon. Dyn., 4 (2000), pp. 170-196.
8. J. T. Cox, A. Greven, and T. Shiga, Finite and infinite systems of interacting diffusions, Probab. Theory Related Fields, 103 (1995), pp. 165-197.
9. S. Deng, K. Giesecke, and T.L. Lai, Sequential importance sampling and resampling for dynamic portfolio credit risk, Oper. Res., 60 (2012), pp. 78-91.
10. T. Eisert and C. Eufinger, Interbank Network and Bank Bailouts: Insurance Mechanism for Noninsured Creditors?, preprint, http://ssrn.com/abstract= 1976383, 2013.
11. K. D. Elworthy, X.-M. Li, and M. Yor, The importance of strictly local martingales; applications to radial Ornstein-Uhlenbeck processes, Probab. Theory Related Fields, 115 (1999), pp. 325-355.
12. P. Erdos and A. Ŕenyi, On random graphs, Publ. Math. Debrecen, 6 (1960), pp. 290-297.
13. J.-P. Fouque and J. Langsam, eds., Handbook on Systemic Risk, Cambridge University Press, Cambridge, UK, 2013.
14. J.-P. Fouque and L.-H. Sun, Systemic risk illustrated, in Handbook on Systemic Risk, J.-P. Fouque and J. Langsam, eds., Cambridge University Press, Cambridge, UK, 2013, pp. 444-452.
15. H. Follmer, Random economics with many interacting agents, J. Math. Econ., 1 (1974), pp. 51-62.
16. J. Garnier, G. Papanicolaou, and T.-W. Yang, Large deviations for a mean field model of systemic risk, SIAM J. Financial Math., 4 (2013), pp. 151-184.
17. K. Giesecke and B. Kim, Systemic risk: What defaults are telling us, Management Sci., 57 (2011), pp. 1387-1405.
18. E.N. Gilbert, Random graphs, Ann. Math. Statist., 30 (1959), pp. 1141-1144.
19. A. Going-Jaeschke and M. Yor, A survey and some generalizations of Bessel processes, Bernoulli, 9 (2003), pp. 313-349.
20. R.Z. Has'minskii, Stochastic Stability of Differential Equations, Sijthoff and Nordhoff, Amsterdam, 1980.
21. T. Ichiba and I. Karatzas, On collisions of Brownian particles, Ann. Appl. Probab., 20 (2010), pp. 951-977.
22. T. Ichiba, V. Papathanakos, A. Banner, I. Karatzas, and R. Fernholz, Hybrid atlas models, Ann. Appl. Probab., 21 (2011), pp. 609-644.
23. N. Ikeda and S. Watanabe, A comparison theorem for solutions of stochastic differential equations and its applications, Osaka J. Math., 14 (1977), pp. 619-633.
24. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed., Grad. Texts in Math. 113, Springer-Verlag, New York, 1991.
25. J. Lorenz, S. Battiston, and F. Schweitzer, Systemic risk in a unifying framework for cascading processes on networks, Eur. Phys. J. B., 71 (2009), pp. 441-460.
26. S.M. Markose, A. Alentorn, and A. Krause, Dynamic Learning, Herding and Guru Effects in Networks, University of Essex, Economics Department Working Paper 582, Essex, UK, 2004.
27. J. Muller, Interbank credit lines as a channel of contagion, J. Financ. Res., 29 (2006), pp. 37-60.
28. E. Nier, J. Yang, T. Yorulmazer, and A. Alentorn, Network models and financial stability, J. Econom. Dynam. Control, 31 (2007), pp. 2033-2060.
29. L.C.G. Rogers and L.A.M. Veraart, Failure and rescue in an interbank network, Management Sci., to appear.
30. E.B. Santos and R. Cont, The Brazilian Interbank Network Structure and Systemic Risk, BancoCentral do Brasil Working Paper 219, Banco Central do Brasil, Brasilia, Brazil, 2010.
31. T. Shiga and A. Shimizu, Infinite-dimensional stochastic differential equations and their applications, J. Math. Kyoto Univ., 20 (1980), pp. 395-416.
32. K. Soramaki, M.L. Bech, J. Arnold, R.J. Glass, and W.E. Beyeler, The topology of interbank payment flows, Phys. A, 379 (2007), pp. 317-333.