Warianty tytułu
Języki publikacji
Abstrakty
The bank run phenomenon, mostly due to rumor spread about the financial health of given financial institutions, is prejudicious to the stability of financial systems. In this paper, by using the epidemiological approach, we propose a nonlinear model for describing the impact of rumor on the banking crisis spread. We establish conditions under which the crisis dies out or remains permanent. We also solve an optimal control problem focusing on the minimization, at the lowest cost, of the number of stressed banks, as well as the number of banks undergoing the restructuring process. Numerical simulations are performed to illustrate theoretical results obtained.
Czasopismo
Rocznik
Tom
Strony
90--118
Opis fizyczny
Bibliogr. 31 poz., tab., wykr.
Twórcy
autor
- Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang-Cameroon, Cameroon, tadmonc@yahoo.fr
- Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang-Cameroon, Cameroon, njikeeric@gmail.com
Bibliografia
- [1] F. Allen and D. Gale, Financial contagion, J. Polit. Econ. 108 (2000), no. 1, 1–33.
- [2] K. Anand, P. Gai, and M. Marsilli, Contagion in financial networks, J. Econom. Dynam. Control 36 (2012), no. 8, 1088–1100.
- [3] E. Nier, J. Yang, and T. Yorulmazer, Network models and financial stability, J. Econom. Dynam. Control 31 (2007), no. 6, 2033–2060.
- [4] B. Martin, T. Stefan, and V. Razvan, Understanding bank-run contagion, ECB Working Paper Number, 1711, 2014.
- [5] B. Fred, Mathematical epidemiology: Past, present, and future, Infect. Dis. Model. 2 (2017), 113–127.
- [6] Z. Ma, X. Jiaotong, and J. Li, Dynamical Modeling and Analysis of Epidemics, World Scientific Publishing, Singapore, 2009.
- [7] J. R. Piquera and V. O. Araujo, A modified epidemiological model for computer viruses, Appl. Math. Comput. 213 (2009), 335–360.
- [8] K. Afassinou, Analysis of the impact of education rate on the rumor spreading mechanism, Phys. A 414 (2014), 43–52.
- [9] Y. Hu, Q. Pan, W. Hou, and M. He, Rumor spreading model considering the proportion of wisemen in crowd, Phys. A 505 (2018), 1084–1094
- [10] M. Li, H. Zhang, P. Georgescu, and T. Li, The stochastic evolution of a rumor spreading model with two distinct spread inhibiting and attitude adjusting mechanisms in a homogeneous social network, Phys. A 562 (2021), 1–24.
- [11] M. Toivanen, Contagion in the interbank network: an epidemiological approach, Bank of Finland Research Discussion Papers, 19, 2003.
- [12] O. Kostylenko, H. S. Rodrigues, and D. F. Torres, Banking risk as an epidemiological model: an optimal control approach, Springer Proc. Math. Stat. 223 (2017), 165–176.
- [13] A. Bucci, D. LaTorre, D. Liuzzi, and S. Marsiglio, Financial contagion and economic development: an epidemiological approach, J. Econ. Behav. Organ. 162 (2019), no. 1, 211–228.
- [14] U. S. code Title 11-Bankruptcy, https://www.law.cornell.edu [Accessed 6 March 2021].
- [15] COBAC, Regulation No 02/14 /CEMAC/ UMAC/COBAC of 25 April 2014, COBAC, 2014.
- [16] W. Wagner, In the quest of systemic externalities: a review of the literature, CESifo Econ. Stud. 56 (2010), no. 1, 96–111.
- [17] J. Müller, Interbank credit lines as a channel of contagion, J. Financial Serv. Res. 29 (2006), no. 1, 37–60.
- [18] D. W. Diamond and P. H. Dybvig, Bank runs, deposit insurance, and liquidity, J. Polit. Econ. 91 (1983), no. 3, 401–419.
- [19] R. J. Caballero and A. Krishnamurthy, Collective risk management in a flight to quality episode, J. Finance 63 (2008), no. 5, 2195–2230.
- [20] S. Brusco and F. Castiglionesi, Liquidity coinsurance, moral hazard, and financial contagion, J. Finance 62 (2000), no. 5, 2275–2302.
- [21] P. Gai and A. H. S. Kapadia, Complexity, concentration and contagion, J. Monet. Econ. 58 (2011), no. 5, 453–470.
- [22] P. Glasserman and H. P. Young, Contagion in financial networks, J. Econ. Lit. 54 (2016), no. 3, 779–831.
- [23] X. Liao, L. Wang, and P. Yu, Stability of dynamical systems, Monograph Series on Nonlinear Science and Complexity, vol. 5, 2007.
- [24] J. K. Hale and S. M. VerduynLunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
- [25] V. Lakshmikantham, S. Leela, and A. A. Matynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker Inc., New York and Basel, 1989.
- [26] D. Philippas, Y. Koutelidakis, and A. Leontitsis, Insights into european interbank network contagion, Manag. Finance 41 (2015), no. 8, 754–772.
- [27] W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, Berlin, 1975.
- [28] H. Gaff and E. Schaefer, Optimal control applied to vaccination and treatment strategies for various epidemiological models, Math. Biosci. Eng. 6 (2009), no. 3, 469–492.
- [29] S. P. Sethi, Optimal Control Theory: Applications to Management Science and Economics, Springer Nature Switzerland AG, 2019.
- [30] J. Zabczyk, Mathematical Control Theory: An Introduction, Birkhäuser, Boston, 1995.
- [31] E. R. Avakov, The maximum principle for abnormal optimal control problems, Akademiia Nauk SSSR Doklady 298 (1988), no. 6, 1289–1292.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-ab542393-bb5d-4626-97a7-c07386313e11