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

Author

Listed:
  • Patrizia Daniele

    (University of Catania)

  • Sofia Giuffrè

    (Mediterranea University of Reggio Calabria)

  • Mariagrazia Lorino

    (University of Catania)

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 $$\rho _j^{*1}(t)$$ ρ j ∗ 1 ( t ) and $$\rho _j^{*2}(t)$$ ρ 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.

Suggested Citation

  • Patrizia Daniele & Sofia Giuffrè & Mariagrazia Lorino, 2016. "Functional inequalities, regularity and computation of the deficit and surplus variables in the financial equilibrium problem," Journal of Global Optimization, Springer, vol. 65(3), pages 575-596, July.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:3:d:10.1007_s10898-015-0382-4
    DOI: 10.1007/s10898-015-0382-4
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    References listed on IDEAS

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    1. P. Daniele & S. Giuffè & M. Lorino & A. Maugeri & C. Mirabella, 2014. "Functional Inequalities and Analysis of Contagion in the Financial Networks," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Handbook of Functional Equations, edition 127, pages 129-146, Springer.
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    4. Barbagallo, Annamaria & Daniele, Patrizia & Giuffrè, Sofia & Maugeri, Antonino, 2014. "Variational approach for a general financial equilibrium problem: The Deficit Formula, the Balance Law and the Liability Formula. A path to the economy recovery," European Journal of Operational Research, Elsevier, vol. 237(1), pages 231-244.
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    7. Annamaria Barbagallo & Paolo Mauro, 2012. "Evolutionary Variational Formulation for Oligopolistic Market Equilibrium Problems with Production Excesses," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 288-314, October.
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