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The Financial Equilibrium Problem with a Markowitz-Type Memory Term and Adaptive Constraints

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  • Patrizia Daniele

    (University of Catania)

  • Mariagrazia Lorino

    (University of Catania)

  • Cristina Mirabella

    (University of Catania)

Abstract

In this paper, we generalize the Markowitz measure of the risk proposed in a stationary setting. We provide an evolutionary Markowitz-type measure of the risk with a memory term and show that this function is effective, namely an existence theorem for the general financial problem can be proved.

Suggested Citation

  • Patrizia Daniele & Mariagrazia Lorino & Cristina Mirabella, 2016. "The Financial Equilibrium Problem with a Markowitz-Type Memory Term and Adaptive Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 276-296, October.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:1:d:10.1007_s10957-016-0973-3
    DOI: 10.1007/s10957-016-0973-3
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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.
    2. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-1297, November.
    3. 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.
    4. Annamaria Barbagallo & Patrizia Daniele & Mariagrazia Lorino & Antonino Maugeri & Cristina Mirabella, 2014. "A Variational Approach to the Evolutionary Financial Equilibrium Problem with Memory Terms and Adaptive Constraints," Springer Optimization and Its Applications, in: Valery A. Kalyagin & Panos M. Pardalos & Themistocles M. Rassias (ed.), Network Models in Economics and Finance, edition 127, pages 13-23, Springer.
    5. A. Nagurney, 2001. "Finance and variational inequalities-super-," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 309-317, March.
    6. Nagurney, Anna, 1994. "Variational inequalities in the analysis and computation of multi-sector, multi-instrument financial equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 161-184, January.
    7. 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.
    8. P. Daniele & A. Maugeri & W. Oettli, 1999. "Time-Dependent Traffic Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 543-555, December.
    9. Patrizia Daniele & Sofia Giuffrè, 2015. "Random Variational Inequalities and the Random Traffic Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 363-381, October.
    10. Ciarcià, Carla & Daniele, Patrizia, 2016. "New existence theorems for quasi-variational inequalities and applications to financial models," European Journal of Operational Research, Elsevier, vol. 251(1), pages 288-299.
    11. Patrizia Daniele, 2006. "Dynamic Networks and Evolutionary Variational Inequalities," Books, Edward Elgar Publishing, number 3516.
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