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Functional inequalities, regularity and computation of the deficit and surplus variables in the financial equilibrium problem

Journal of Global Optimization volume 65, pages 575–596 (2016)Cite this article

Abstract

This paper is concerned with a general model of financial flows and prices related to individual entities, called sectors, which invest in financial instruments as assets and as liabilities. In particular, using delicate tools of Functional Analysis, besides existence results of financial equilibrium, in the dual formulation, the Lagrange functions \(\rho _j^{*1}(t)\) and \(\rho _j^{*2}(t)\), called “deficit” and “surplus” variables, appear and reveal to be very relevant in order to analyze the financial model and the possible insolvencies, which can lead to a financial contagion. In the paper the continuity of these Lagrange functions is proved. Finally, a procedure for the calculus of these variables is suggested.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, University of Catania, Viale A. Doria, 6, 95125, Catania, Italy

    Patrizia Daniele & Mariagrazia Lorino

  2. D.I.I.E.S, Mediterranea University of Reggio Calabria, Località Feo di Vito, 89122, Reggio Calabria, Italy

    Sofia Giuffrè

Authors
  1. Patrizia Daniele
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  2. Sofia Giuffrè
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  3. Mariagrazia Lorino
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Correspondence to Sofia Giuffrè.

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Daniele, P., Giuffrè, S. & Lorino, M. Functional inequalities, regularity and computation of the deficit and surplus variables in the financial equilibrium problem. J Glob Optim 65, 575–596 (2016). https://doi.org/10.1007/s10898-015-0382-4

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  • DOI: https://doi.org/10.1007/s10898-015-0382-4

Keywords

  • Financial problem
  • Variational inequality formulation
  • Equilibrium conditions
  • Dual Lagrange formulation
  • Deficit and surplus variables
  • Financial contagion

Mathematics Subject Classification

  • 90B50
  • 49J40
  • 91G80