Banking Risk as an Epidemiological Model: An Optimal Control Approach

  • Olena Kostylenko
  • Helena Sofia Rodrigues
  • Delfim F. M. Torres
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 223)


The process of contagiousness spread modelling is well-known in epidemiology. However, the application of spread modelling to banking market is quite recent. In this work, we present a system of ordinary differential equations, simulating data from the largest European banks. Then, an optimal control problem is formulated in order to study the impact of a possible measure of the Central Bank in the economy. The proposed approach enables qualitative specifications of contagion in banking obtainment and an adequate analysis and prognosis within the financial sector development and macroeconomy as a whole. We show that our model describes well the reality of the largest European banks. Simulations were done using MATLAB and BOCOP optimal control solver, and the main results are taken for three distinct scenarios.


Banking risk Contagion spread Epidemic approach Optimal control 



This research was supported in part by the Portuguese Foundation for Science and Technology (FCT – Fundação para a Ciência e a Tecnologia), through CIDMA – Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013. Kostylenko is also supported by the Ph.D. fellowship PD/BD/114188/2016. We are very grateful to the authors of [19] for providing us the parameter values that they have obtained in their work; and to two anonymous referees for valuable remarks and comments, which significantly contributed to the quality of the paper.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Olena Kostylenko
    • 1
  • Helena Sofia Rodrigues
    • 2
  • Delfim F. M. Torres
    • 1
  1. 1.Center for Research and Development in Mathematics and Applications (CIDMA), Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Center for Research and Development in Mathematics and Applications (CIDMA)School of Business Studies, Polytechnic Institute of Viana do CasteloValençaPortugal

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