Variational Inequalities for Time Dependent Financial Equilibrium with Price Constraints

  • S. Giuffrè
  • S. Pia
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 79)


We study a financial evolutionary problem, when variance-covariance matrices, sector financial holding volumes, instrument prices are time-dependent. As in P.Daniele [1], but assuming the realistic condition of a lower constraint for the price of each instrument, we give the evolutionary financial equilibrium condition, prove an equivalent variational inequality formulation and an existence result.

Key words

financial problem equilibrium condition variational inequality formulation time-dependent requirements 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P. Daniele, Variational Inequalities for Evolutionary Financial Equilibrium, Advances in Economic and Financial Networks, A. Nagurney Ed. (2003), 84–108.Google Scholar
  2. [2]
    P. Daniele, Lagrangean Funtion for Dynamic Variational Inequalities, Rendiconti del Circolo Matematico di Palermo, Serie II, Suppl. 58, 101–119.Google Scholar
  3. [3]
    J. Dong, D. Zhang and A. Nagurney, A projected Dynamical Systems Model of General Financial Equilibrium with Stability Analysis, Mathematical and Computer Modeling 24 (1996), 35–44.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    J. Jahn, Introduction to the Theory of Nonlinear Optimization, Springer-Verlag, Berlin, 1996.zbMATHGoogle Scholar
  5. [5]
    H.M. Markowitz, Portfolio Selection, Journal of Finance 7 (1952), 77–91.CrossRefGoogle Scholar
  6. [6]
    H.M. Markowitz, Portfolio Selection: Efficient Diversification of Investments, Wiley & Sons, New York, 1959.Google Scholar
  7. [7]
    A. Nagurney, Variational Inequalities in the Analysis and Computation of Multi-Sector Multi-Instrument Financial Equilibria, Journal of Economic Dynamics and Control 18 (1994), 161–184.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    A. Nagurney, Network Economics-A Variational Inequality Approach, second and revised version, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.Google Scholar
  9. [9]
    A. Nagurney, Financial and Variational Inequalities, Quantitative Finance 1 (2001), 309–317.CrossRefMathSciNetGoogle Scholar
  10. [10]
    A. Nagurney, J. Dong and M. Hughes, Formulation and Computation of General Financial Equilibrium, Optimization 26 (1992), 339–354.zbMATHMathSciNetGoogle Scholar
  11. [11]
    A. Nagumey and K. Ke, Financial Networks with Intermediation, Quantitative Finance 1 (2001), 441–451.CrossRefMathSciNetGoogle Scholar
  12. [12]
    A. Nagumey and S. Siokos, Variational Inequalities for International General Financial Equilibrium Modeling and Computation, Mathematical and Computer Modelling 25 (1997), 31–49.Google Scholar
  13. [13]
    A. Nagurney and S. Siokos, Financial Networks: Statics and Dynamics, Springer-Verlag, Heidelberg, Germany, 1997.Google Scholar
  14. [14]
    A. Nagurney and D. Zhang, Projected Dynamical Systems and Variational Inequalities with Applications, Kluwer Academic Publishers, Boston, Massachussets, 1996.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • S. Giuffrè
    • 1
  • S. Pia
    • 1
  1. 1.D.I.M.E.T., Faculty of EngineeringUniversity of Reggio CalabriaReggio CalabriaItaly

Personalised recommendations