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Handbook of Functional Equations pp 129–146Cite as

Functional Inequalities and Analysis of Contagion in the Financial Networks

Part of the Springer Optimization and Its Applications book series (SOIA,volume 95)

Abstract

In very recent papers, using delicate tools of functional analysis, a general equilibrium model of financial flows and prices is studied. In particular, without using a technical language, but using the universal language of mathematics, some significant laws, such as the Deficit formula, the Balance law and the Liability formula for the management of the world economy are provided. Further a simple but useful economical indicator E(t) is considered. In this paper, considering the Lagrange dual formulation of the financial model, the Lagrange variables called “deficit” and “surplus” variables are considered. By means of these variables, we study the possible insolvencies related to the financial instruments and their propagation to the entire system, producing a “financial contagion”.

Keywords

  • Financial networks
  • Deficit and surplus variables
  • Shadow market
  • Balance law
  • Financial contagion

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References

  1. Barbagallo, A.: On the regularity of retarded equilibria in time-dependent traffic equilibrium problems. Nonlinear Anal. Theory Appl. 71(12), e2406–e2417 (2009)

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. Barbagallo, A., Di Vincenzo, R.: Lipschitz continuity and duality. J. Math. Anal. Appl. 382(1), 231–247 (2011)

    CrossRef  MATH  MathSciNet  Google Scholar 

  3. Barbagallo, A., Maugeri, A.: Duality theory for the dynamic oligopolistic market equilibrium problem. Optimization 60, 29–52 (2011)

    CrossRef  MATH  MathSciNet  Google Scholar 

  4. Barbagallo, A., Daniele, P., Maugeri, A.: Variational formulation for a general dynamic financial equilibrium problem: Balance law and liability formula. Nonlinear Anal. Theory Appl. 75(3), 1104–1123 (2012)

    CrossRef  MATH  MathSciNet  Google Scholar 

  5. Barbagallo, A., Daniele, P., Lorino, M., Maugeri, A., Mirabella, C.: Further results for general financial equilibrium problems via variational inequalities. J. Math. Financ. 3(1), 33–52 (2013)

    CrossRef  Google Scholar 

  6. Barbagallo, A., Daniele, P., Giuffrè, S., Maugeri, A.: Variational approach for a general financial equilibrium problem. The deficit formula, the balance law and the liability formula. A path to the recovery. Eur. J. Oper. Res. 237(1), 231–244 (2014)

    CrossRef  Google Scholar 

  7. Barbagallo, A., Daniele, P., Lorino, M., Maugeri, A., Mirabella, C.: A Variational approach to the evolutionary financial equilibrium problem with memeory terms and adaptive constraints. Submitted to Network Models in Economics and Finance 2013, Springer Optimization and Its Applications.

    Google Scholar 

  8. Cojocaru, M.-G., Daniele, P., Nagurney, A.: Double-layered dynamics: A unified theory of projected dynamical systems and evolutionary variational inequalities. Eur. J. Oper. Res. 175(1), 494–507 (2006)

    CrossRef  MATH  MathSciNet  Google Scholar 

  9. Daniele, P.: Variational inequalities for evolutionary financial equilibrium. In: Nagurney, A. (ed.) Innovations in Financial and Economic Networks, 84–108, (2003)

    Google Scholar 

  10. Daniele, P.: Variational inequalities for general evolutionary financial equilibrium. In: Giannessi, F., Maugeri, A. (eds.) Variational Analysis and Applications. Springer, 279–299 (2003)

    Google Scholar 

  11. Daniele, P.: Evolutionary variational inequalities applied to financial equilibrium problems in an environment of risk and uncertainty. Nonlinear Anal. Theory Appl. 63, 1645–1653 (2005)

    CrossRef  Google Scholar 

  12. Daniele, P.: Dynamic Networks and Evolutionary Variational Inequalities. Edward Elgar Publishing, Chentelham (2006)

    MATH  Google Scholar 

  13. Daniele, P.: Evolutionary variational inequalities and applications to complex dynamic multi-level models. Transport. Res. Part E 46(6), 855–880 (2010). doi:10.1016/j.tre.2010.03.005.

    CrossRef  Google Scholar 

  14. Daniele, P., Giuffrè, S.: General infinite dimensional duality and applications to evolutionary network equilibrium problems. Optim. Lett. 1(3), 227–243 (2007)

    CrossRef  MATH  MathSciNet  Google Scholar 

  15. Daniele, P., Giuffrè, S., Pia, S.: Competitive financial equilibrium problems with policy interventions. J. Ind. Manag. Optim. 1(1), 39–52 (2005)

    CrossRef  MATH  MathSciNet  Google Scholar 

  16. Daniele, P., Giuffrè, S., Idone, G., Maugeri, A.: Infinite dimensional duality and applications. Math. Ann. 339(1), 221–239 (2007)

    CrossRef  MATH  MathSciNet  Google Scholar 

  17. Daniele, P., Giuffrè, S., Maugeri, A.: Remarks on general infinite dimensional duality with cone and equality constraints. Commun. Appl Anal. 13(4), 567–578 (2009)

    MATH  MathSciNet  Google Scholar 

  18. Dong, J., Zhang, D., Nagurney, A.: A projected dynamical systems model of general financial equilibrium with stability analysis. Math. Comput. Model. 24(2), 35–44 (1996)

    CrossRef  MATH  MathSciNet  Google Scholar 

  19. Fucik, S., Kufner, A.: Nonlinear Ddifferential Eequations. Elsevier Sci. Publ. Co., New York (1980)

    Google Scholar 

  20. Giuffrè, S., Pia, S.: Weighted traffic equilibrium problem in non pivot Hilbert spaces. Nonlinear Anal. Theory Appl. 71, e2054–e2061 (2009)

    CrossRef  MATH  Google Scholar 

  21. Giuffrè, S., Pia, S.: Weighted Traffic Equilibrium Problem in Non Pivot Hilbert Spaces with Long Term Memory. In: AIP Conference Proceedings Rodi, September 2010, vol. 1281, 282–285.

    Google Scholar 

  22. Giuffrè, S., Idone, G., Pia, S.: Some classes of projected dynamical systems in Banach spaces and variational inequalities. J. Global Optim. 40(1–3), 119–128 (2008)

    CrossRef  MATH  MathSciNet  Google Scholar 

  23. Jahn, J.: Introduction to the Theory of Nonlinear Optimization. Springer-Verlag, Berlin (1996)

    CrossRef  MATH  Google Scholar 

  24. Jaillet, P., Lamberton, D., Lapeyre, B.: Variational inequalities and the pricing of American options. Acta Appl. Math. 21(3), 253–289 (1990)

    CrossRef  MathSciNet  Google Scholar 

  25. Markowitz, H.M.: Portfolio selection. J. Finance 7(1), 77–91 (1952)

    Google Scholar 

  26. Markowitz, H.M.: Portfolio Selection: Efficient Diversification of Investments. Wiley, New York (1959)

    Google Scholar 

  27. Maugeri, A., Raciti, F.: On existence theorems for monotone and nonmonotone variational inequalities. J. Convex Anal. 16, 899–911 (2009)

    MATH  MathSciNet  Google Scholar 

  28. Maugeri, A., Raciti, F.: Remarks on infinite dimensional duality. J. Global Optim. 46(4), 581–588 (2010)

    CrossRef  MATH  MathSciNet  Google Scholar 

  29. Maugeri, A., Scrimali, L.: Global lipschitz continuity of solutions to parameterized variational inequalities. Boll. Unione Mat. Italiana 9(2), 45–69 (2009)

    MathSciNet  Google Scholar 

  30. Nagurney, A.: Variational inequalities in the analysis and computation of multi-sector, multi-instrument financial equilibria. J. Econ. Dyn. Control 18(1), 161–184 (1994)

    CrossRef  MATH  MathSciNet  Google Scholar 

  31. Nagurney, A.: Finance and variational inequalities. Quant. Finance 1(3), 309–317 (2001)

    CrossRef  MathSciNet  Google Scholar 

  32. Nagurney, A., Siokos, S.: Variational inequalities for international general financial equilibrium modeling and computation. Math. Comput. Modell. 25(1), 31–49 (1997)

    CrossRef  MATH  MathSciNet  Google Scholar 

  33. Nagurney, A., Siokos, S.: Financial Networks: Statics and Dynamics. Springer, Heidelberg (1997)

    CrossRef  Google Scholar 

  34. Nagurney, A., Dong, J. Hughes, M.: Formulation and computation of general financial equilibrium. Optim. J. Math. Program. Oper. Res. 26(3), 339–354 (1992)

    MATH  MathSciNet  Google Scholar 

  35. Stampacchia, G.: Variational Inequalities, theory and applications of monotone operators, Proceedings of a NATO Advanced Study Institute (Venice, 1968), Oderisi, Gubbio, 101–192, (1969)

    Google Scholar 

  36. Tourin, A., Zariphopoulou, T.: Numerical schemes for investment models with singular transactions. Comput. Econ. 7(4), 287–307 (1994)

    CrossRef  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

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

    P. Daniele, M. Lorino, A. Maugeri & C. Mirabella

  2. D.I.M.E.T. Faculty of Engineering, University of Reggio Calabria, 89060, Reggio Calabria, Italy

    S. Giuffè

Authors
  1. P. Daniele
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  2. S. Giuffè
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  3. M. Lorino
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  4. A. Maugeri
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  5. C. Mirabella
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Corresponding author

Correspondence to P. Daniele .

Editor information

Editors and Affiliations

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

    Themistocles M. Rassias

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Daniele, P., Giuffè, S., Lorino, M., Maugeri, A., Mirabella, C. (2014). Functional Inequalities and Analysis of Contagion in the Financial Networks. In: Rassias, T. (eds) Handbook of Functional Equations. Springer Optimization and Its Applications, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1246-9_7

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