IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i2p425-d1034694.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/2/425/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/2/425/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. Lian, Yili, 2017. "Financial distress and customer-supplier relationships," Journal of Corporate Finance, Elsevier, vol. 43(C), pages 397-406.
    5. 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.
    6. 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.
    7. Ana Babus, 2016. "The formation of financial networks," RAND Journal of Economics, RAND Corporation, vol. 47(2), pages 239-272, May.
    8. 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.
    9. Marangi, Carmela & Martiradonna, Angela & Ragni, Stefania, 2023. "Optimal resource allocation for spatiotemporal control of invasive species," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    10. 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.
    11. 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.
    12. 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).
    13. 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).
    14. Philippe Jorion & Gaiyan Zhang, 2009. "Credit Contagion from Counterparty Risk," Journal of Finance, American Finance Association, vol. 64(5), pages 2053-2087, October.
    15. 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.
    16. Andrew G. Haldane & Robert M. May, 2011. "Systemic risk in banking ecosystems," Nature, Nature, vol. 469(7330), pages 351-355, January.
    17. 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.
    18. 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.
    19. 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).
    20. 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.
    21. 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).
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Willi Semmler & Fabio Della Rossa & Giuseppe Orlando & Gabriel R. Padro Rosario & Levent Kockesen, 2023. "Endogenous Economic Resilience, Loss of Resilience, Persistent Cycles, Multiple Attractors, and Disruptive Contractions," Working Papers 2309, New School for Social Research, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Calabrese, Raffaella, 2023. "Contagion effects of UK small business failures: A spatial hierarchical autoregressive model for binary data," European Journal of Operational Research, Elsevier, vol. 305(2), pages 989-997.
    2. Qian, Qian & Chao, Xiangrui & Feng, Hairong, 2023. "Internal or external control? How to respond to credit risk contagion in complex enterprises network," International Review of Financial Analysis, Elsevier, vol. 87(C).
    3. Azizpour, S & Giesecke, K. & Schwenkler, G., 2018. "Exploring the sources of default clustering," Journal of Financial Economics, Elsevier, vol. 129(1), pages 154-183.
    4. 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).
    5. Tingqiang Chen & Binqing Xiao & Haifei Liu, 2018. "Credit Risk Contagion in an Evolving Network Model Integrating Spillover Effects and Behavioral Interventions," Complexity, Hindawi, vol. 2018, pages 1-16, March.
    6. Qian Qian & Yang Yang & Zong-Fang Zhou, 2019. "Research on Trade Credit Spreading and Credit Risk within the Supply Chain," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 389-411, January.
    7. Edirisinghe, Chanaka & Gupta, Aparna & Roth, Wendy, 2015. "Risk assessment based on the analysis of the impact of contagion flow," Journal of Banking & Finance, Elsevier, vol. 60(C), pages 209-223.
    8. 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.
    9. Andre R. Neveu, 2018. "A survey of network-based analysis and systemic risk measurement," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 13(2), pages 241-281, July.
    10. Tingqiang Chen & Xindan Li & Jining Wang, 2015. "Spatial Interaction Model of Credit Risk Contagion in the CRT Market," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 519-537, December.
    11. Wong, Kacheng & Zhao, Longkai, 2023. "Customer–supplier relationships and non-linear financial policy response," Journal of Empirical Finance, Elsevier, vol. 73(C), pages 180-205.
    12. Dan Dhaliwal & Paul N. Michas & Vic Naiker & Divesh Sharma, 2020. "Greater Reliance on Major Customers and Auditor Going‐Concern Opinions," Contemporary Accounting Research, John Wiley & Sons, vol. 37(1), pages 160-188, March.
    13. Chen, Tingqiang & Wang, Jiepeng & Liu, Haifei & He, Yuanping, 2019. "Contagion model on counterparty credit risk in the CRT market by considering the heterogeneity of counterparties and preferential-random mixing attachment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 458-480.
    14. Burney, Robert B. & James, Hui Liang & Wang, Hongxia, 2021. "Working capital management and CEO age," Journal of Behavioral and Experimental Finance, Elsevier, vol. 30(C).
    15. Dirk Helbing, 2013. "Economics 2.0: The Natural Step towards A Self-Regulating, Participatory Market Society," Papers 1305.4078, arXiv.org, revised Jun 2013.
    16. Michi Nishihara & Takashi Shibata, 2020. "Optimal capital structure and bankruptcy cascades," Discussion Papers in Economics and Business 20-10, Osaka University, Graduate School of Economics.
    17. Chatjuthamard, Pattanaporn & Kijkasiwat, Ploypailin & Jiraporn, Pornsit & Lee, Sang Mook, 2023. "Customer concentration, managerial risk aversion, and independent directors: A quasi-natural experiment," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 358-368.
    18. Nina Boyarchenko & Anna M. Costello, 2014. "Counterparty risk in material supply contracts," Staff Reports 694, Federal Reserve Bank of New York.
    19. Manh Cuong Nguyen & Viet Anh Dang & Tri Tri Nguyen, 2023. "The transfer of risk taking along the supply chain," Review of Quantitative Finance and Accounting, Springer, vol. 61(4), pages 1341-1378, November.
    20. Ulrich Horst & Wei Xu, 2024. "Functional Limit Theorems for Hawkes Processes," Papers 2401.11495, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:425-:d:1034694. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.