IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p998-d1069884.html
   My bibliography  Save this article

Influence of the Internal Structure on the Integral Risk of a Complex System on the Example of the Risk Minimization Problem in a “Star” Type Structure

Author

Listed:
  • Alexander Shiroky

    (V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia)

  • Andrey Kalashnikov

    (V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia)

Abstract

This paper is devoted to studying the influence of the structure of a complex system on its integral risk. When solving risk management problems, it often becomes necessary to take into account structural effects, which most often include risk transfer and failure propagation. This study discusses the influence of the position of the elements of a protected system inside a fixed structure of the “star” type on its integral risk. The authors demonstrate that the problem of the optimal placement of elements in such a structure from the point of view of minimizing the risk cannot be precisely solved by analytical methods and propose an algorithm for solving it with bounded errors. For the case of equal expected damages in case of a successful attack of a system element, the authors calculate upper estimates for the relative error of solving the placement problem using the proposed algorithm and also propose a methodology for rapid risk assessment for systems with a “star” type structure. Finally, for the particular case when the risks of elements are in a certain ratio, the authors have found an exact solution to the problem of the optimal placement of elements.

Suggested Citation

  • Alexander Shiroky & Andrey Kalashnikov, 2023. "Influence of the Internal Structure on the Integral Risk of a Complex System on the Example of the Risk Minimization Problem in a “Star” Type Structure," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:998-:d:1069884
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/998/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/4/998/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dagmawi Mulugeta Degefu & Weijun He & Liang Yuan, 2017. "Monotonic Bargaining Solution for Allocating Critically Scarce Transboundary Water," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2627-2644, July.
    2. D. O. Cajueiro & R.F.S. Andrade, 2010. "Controlling self-organized criticality in complex networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 77(2), pages 291-296, September.
    3. Clemente, G.P. & Grassi, R., 2018. "Directed clustering in weighted networks: A new perspective," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 26-38.
    4. Regino Criado & Miguel Romance, 2012. "Structural Vulnerability and Robustness in Complex Networks: Different Approaches and Relationships Between them," Springer Optimization and Its Applications, in: My T. Thai & Panos M. Pardalos (ed.), Handbook of Optimization in Complex Networks, chapter 0, pages 3-36, Springer.
    5. Pu, Cun-Lai & Cui, Wei, 2015. "Vulnerability of complex networks under path-based attacks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 622-629.
    6. Chen Chen & Garud Iyengar & Ciamac C. Moallemi, 2013. "An Axiomatic Approach to Systemic Risk," Management Science, INFORMS, vol. 59(6), pages 1373-1388, June.
    Full references (including those not matched with items on IDEAS)

    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. Vikram Bharti & Thendiyath Roshni & Madan Kumar Jha & Mohammad Ali Ghorbani & Osama Ragab Abdelaziz Ibrahim, 2024. "Complex network analysis of groundwater level in Sina Basin, Maharashtra, India," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 26(7), pages 18017-18032, July.
    2. Christophe Chorro & Emmanuelle Jay & Philippe De Peretti & Thibault Soler, 2021. "Frequency causality measures and Vector AutoRegressive (VAR) models: An improved subset selection method suited to parsimonious systems," Documents de travail du Centre d'Economie de la Sorbonne 21013, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Wang, Wei & Xu, Huifu & Ma, Tiejun, 2023. "Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 322-347.
    4. Roy Cerqueti & Francesca Pampurini & Annagiulia Pezzola & Anna Grazia Quaranta, 2022. "Dangerous liasons and hot customers for banks," Review of Quantitative Finance and Accounting, Springer, vol. 59(1), pages 65-89, July.
    5. Francesca Biagini & Andrea Mazzon & Thilo Meyer-Brandis, 2018. "Financial asset bubbles in banking networks," Papers 1806.01728, arXiv.org.
    6. Hougaard, Jens Leth & Smilgins, Aleksandrs, 2016. "Risk capital allocation with autonomous subunits: The Lorenz set," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 151-157.
    7. Christian Kubitza, 2021. "Tackling the Volatility Paradox: Spillover Persistence and Systemic Risk," ECONtribute Discussion Papers Series 079, University of Bonn and University of Cologne, Germany.
    8. Oliver Kley & Claudia Kluppelberg, 2015. "Bounds for randomly shared risk of heavy-tailed loss factors," Papers 1503.03726, arXiv.org, revised Apr 2016.
    9. Viljoen, Nadia M. & Joubert, Johan W., 2016. "The vulnerability of the global container shipping network to targeted link disruption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 396-409.
    10. Nadia von Jacobi & Vito Amendolagine, 2021. "What Feeds on What? Networks of Interdependencies between Culture and Institutions," DEM Working Papers 2021/13, Department of Economics and Management.
    11. Hans Buhl, 2013. "IT as Curse and Blessing," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 5(6), pages 377-381, December.
    12. Fabrizio Fusillo & Sandro Montresor & Giuseppe Vittucci Marzetti, 2021. "The global network of embodied R&D flows," Discussion Paper series in Regional Science & Economic Geography 2021-05, Gran Sasso Science Institute, Social Sciences, revised Apr 2021.
    13. Ludger Overbeck & Florian Schindler, 2021. "Scalar systemic risk measures and Aumann-Shapley allocations," Papers 2112.06534, arXiv.org, revised Jul 2022.
    14. Timo Dimitriadis & Yannick Hoga, 2022. "Dynamic CoVaR Modeling and Estimation," Papers 2206.14275, arXiv.org, revised Jan 2025.
    15. Péter Csóka & P. Jean-Jacques Herings, 2018. "Decentralized Clearing in Financial Networks," Management Science, INFORMS, vol. 64(10), pages 4681-4699, October.
    16. Erhan Bayraktar & Gaoyue Guo & Wenpin Tang & Yuming Paul Zhang, 2022. "Systemic robustness: a mean-field particle system approach," Papers 2212.08518, arXiv.org, revised Aug 2023.
    17. Wang, Tao & Xiao, Shiying & Yan, Jun & Zhang, Panpan, 2021. "Regional and sectoral structures of the Chinese economy: A network perspective from multi-regional input–output tables," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    18. Hannes Hoffmann & Thilo Meyer-Brandis & Gregor Svindland, 2016. "Risk-Consistent Conditional Systemic Risk Measures," Papers 1609.07897, arXiv.org.
    19. Hamed Amini & Zachary Feinstein, 2020. "Optimal Network Compression," Papers 2008.08733, arXiv.org, revised Jul 2022.
    20. Kashin Sugishita & Yasuo Asakura, 2021. "Vulnerability studies in the fields of transportation and complex networks: a citation network analysis," Public Transport, Springer, vol. 13(1), pages 1-34, March.

    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:4:p:998-:d:1069884. 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.