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A Variational Approach to the Financial Problem with Insolvencies and Analysis of the Contagion

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Mathematical Analysis and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 154))

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Abstract

In this chapter we improve some results in literature on the general financial equilibrium problem related to individual entities, called sectors, which invest in financial instruments as assets and as liabilities. Indeed the model, studied in the chapter, takes into account the insolvencies and we analyze how these insolvencies affect the financial problem. For this improved model we describe a variational inequality for which we provide an existence result. Moreover, we study the dual Lagrange problem, in which the Lagrange variables, which represent the deficit and the surplus per unit, appear and an economical indicator is provided. Finally, we perform the contagion by means of the deficit and surplus variables. As expected, the presence of the insolvencies makes it more difficult to reach the financial equilibrium and increases the risk of a negative contagion for all the systems.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    Giorgia Cappello, Patrizia Daniele & Antonino Maugeri

  2. D.I.I.E.S. “Mediterranea” University of Reggio Calabria, Reggio Calabria, Italy

    Sofia Giuffrè

Authors
  1. Giorgia Cappello
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  2. Patrizia Daniele
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  3. Sofia Giuffrè
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  4. Antonino Maugeri
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Corresponding author

Correspondence to Patrizia Daniele .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Cappello, G., Daniele, P., Giuffrè, S., Maugeri, A. (2019). A Variational Approach to the Financial Problem with Insolvencies and Analysis of the Contagion. In: Rassias, T., Pardalos, P. (eds) Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 154. Springer, Cham. https://doi.org/10.1007/978-3-030-31339-5_2

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