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A Dynamical Model with Time Delay for Risk Contagion

Author

Listed:
  • Mauro Aliano

    (Department of Economics and Management, University of Ferrara, 44121 Ferrara, Italy)

  • Lucianna Cananà

    (Ionic Department in Legal and Economic Systems of the Mediterranean: Society, Environment, Culture, University of Bari Aldo Moro, 74121 Taranto, Italy)

  • Greta Cestari

    (Department of Economics and Management, University of Ferrara, 44121 Ferrara, Italy)

  • Stefania Ragni

    (Department of Economics and Management, University of Ferrara, 44121 Ferrara, Italy)

Abstract

The explanation of risk contagion among economic players—not only in financial crises—and how they spread across the world has fascinated scholars and scientists in the last few decades. Inspired by the literature dealing with the analogy between financial systems and ecosystems, we model risk contagion by revisiting the mathematical approach of epidemiological models for infectious disease spread in a new paradigm. We propose a time delay differential system describing risk diffusion among companies inside an economic sector by means of a SIR dynamics. Contagion is modelled in terms of credit and financial risks with low and high levels. A complete theoretical analysis of the problem is carried out: well-posedness and solution positivity are proven. The existence of a risk-free steady state together with an endemic equilibrium is verified. Global asymptotic stability is investigated for both equilibria by the classical Lyapunov functional theory. The model is tested on a case study of some companies operating in the food economic sector in a specific Italian region. The analysis allows for understanding the crucial role of both incubation time and financial immunity period in the asymptotic behaviour of any solution in terms of endemic permanence of risk rather than its disappearance.

Suggested Citation

  • Mauro Aliano & Lucianna Cananà & Greta Cestari & Stefania Ragni, 2023. "A Dynamical Model with Time Delay for Risk Contagion," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:425-:d:1034694
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    References listed on IDEAS

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    1. Adekoya, Oluwasegun B. & Oliyide, Johnson A., 2022. "Commodity and financial markets’ fear before and during COVID-19 pandemic: Persistence and causality analyses," Resources Policy, Elsevier, vol. 76(C).
    2. Barro, Diana & Basso, Antonella, 2010. "Credit contagion in a network of firms with spatial interaction," European Journal of Operational Research, Elsevier, vol. 205(2), pages 459-468, September.
    3. George A. Akerlof, 2009. "How Human Psychology Drives the Economy and Why It Matters," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(5), pages 1175-1175.
    4. Maté-Sánchez-Val, Mariluz & López-Hernandez, Fernando & Rodriguez Fuentes, Christian Camilo, 2018. "Geographical factors and business failure: An empirical study from the Madrid metropolitan area," Economic Modelling, Elsevier, vol. 74(C), pages 275-283.
    5. Leonidov, A.V. & Rumyantsev, E.L., 2016. "Default contagion risks in Russian interbank market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 36-48.
    6. Lian, Yili, 2017. "Financial distress and customer-supplier relationships," Journal of Corporate Finance, Elsevier, vol. 43(C), pages 397-406.
    7. Fernandes, Guilherme Barreto & Artes, Rinaldo, 2016. "Spatial dependence in credit risk and its improvement in credit scoring," European Journal of Operational Research, Elsevier, vol. 249(2), pages 517-524.
    8. Andrew G. Haldane & Robert M. May, 2011. "Systemic risk in banking ecosystems," Nature, Nature, vol. 469(7330), pages 351-355, January.
    9. Ana Babus, 2016. "The formation of financial networks," RAND Journal of Economics, RAND Corporation, vol. 47(2), pages 239-272, May.
    10. Fanelli, Viviana & Maddalena, Lucia, 2020. "A nonlinear dynamic model for credit risk contagion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 45-58.
    11. Jiang, Shanshan & Fan, Hong, 2018. "Credit risk contagion coupling with sentiment contagion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 186-202.
    12. Zhao, Chengguo & Li, Meng & Wang, Jun & Ma, Shujian, 2021. "The mechanism of credit risk contagion among internet P2P lending platforms based on a SEIR model with time-lag," Research in International Business and Finance, Elsevier, vol. 57(C).
    13. Economou, Fotini & Panagopoulos, Yannis & Tsouma, Ekaterini, 2018. "Uncovering asymmetries in the relationship between fear and the stock market using a hidden co-integration approach," Research in International Business and Finance, Elsevier, vol. 44(C), pages 459-470.
    14. Hertzel, Michael G. & Li, Zhi & Officer, Micah S. & Rodgers, Kimberly J., 2008. "Inter-firm linkages and the wealth effects of financial distress along the supply chain," Journal of Financial Economics, Elsevier, vol. 87(2), pages 374-387, February.
    15. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    16. Shi, Qing & Sun, Xiaoqi & Jiang, Yile, 2022. "Concentrated commonalities and systemic risk in China's banking system: A contagion network approach," International Review of Financial Analysis, Elsevier, vol. 83(C).
    17. Marangi, Carmela & Martiradonna, Angela & Ragni, Stefania, 2023. "Optimal resource allocation for spatiotemporal control of invasive species," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    18. Raffaella Calabrese & Galina Andreeva & Jake Ansell, 2019. "“Birds of a Feather” Fail Together: Exploring the Nature of Dependency in SME Defaults," Risk Analysis, John Wiley & Sons, vol. 39(1), pages 71-84, January.
    19. Egloff, Daniel & Leippold, Markus & Vanini, Paolo, 2007. "A simple model of credit contagion," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2475-2492, August.
    20. Xie, Xiaofeng & Shi, Xinyu & Gu, Jing & Xu, Xun, 2023. "Examining the Contagion Effect of Credit Risk in a Supply Chain under Trade Credit and Bank Loan Offering," Omega, Elsevier, vol. 115(C).
    21. Torri, Gabriele & Radi, Davide & Dvořáčková, Hana, 2022. "Catastrophic and systemic risk in the non-life insurance sector: A micro-structural contagion approach," Finance Research Letters, Elsevier, vol. 47(PB).
    22. Philippe Jorion & Gaiyan Zhang, 2009. "Credit Contagion from Counterparty Risk," Journal of Finance, American Finance Association, vol. 64(5), pages 2053-2087, October.
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