IDEAS home Printed from https://ideas.repec.org/a/ibn/jmrjnl/v10y2018i1p115.html
   My bibliography  Save this article

Asymptotic Analysis of a Deterministic Control System via Euler's Equation Approach

Author

Listed:
  • Gladys Denisse Salgado Su¨¢rez
  • Hugo Cruz-Su¨¢rez
  • Jos¨¦ Dionicio Zacar¨ªas Flores

Abstract

This paper provides necessary conditions in order to guarantee the existence of an unique equilibrium point in a deterministic control system. Furthermore, under additional conditions, it is proved the convergence of the optimal control sequence to this equilibrium point. The methodology to obtain these statements is based on the Euler's equation approach. A consumption-investment problem is presented with the objective to illustrate the results exposed.

Suggested Citation

  • Gladys Denisse Salgado Su¨¢rez & Hugo Cruz-Su¨¢rez & Jos¨¦ Dionicio Zacar¨ªas Flores, 2018. "Asymptotic Analysis of a Deterministic Control System via Euler's Equation Approach," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(1), pages 115-123, February.
    • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:1:p:115
    as

    Download full text from publisher

    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/73037/40102
    Download Restriction: no
    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/73037
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fuente,Angel de la, 2000. "Mathematical Methods and Models for Economists," Cambridge Books, Cambridge University Press, number 9780521585293.
    2. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    3. Daniel Cruz-Suárez & Raúl Montes-de-Oca & Francisco Salem-Silva, 2004. "Conditions for the uniqueness of optimal policies of discounted Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 415-436, December.
    4. Hugo Cruz-Suárez & Raúl Montes-de-Oca, 2008. "An envelope theorem and some applications to discounted Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 299-321, April.
    5. Zhang, Jinqing & Jin, Zeyu & An, Yunbi, 2017. "Dynamic portfolio optimization with ambiguity aversion," Journal of Banking & Finance, Elsevier, vol. 79(C), pages 95-109.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    2. Hugo Cruz-Suárez & Raúl Montes-de-Oca, 2008. "An envelope theorem and some applications to discounted Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 299-321, April.
    3. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2014. "Approximate dynamic programming for stochastic N-stage optimization with application to optimal consumption under uncertainty," Computational Optimization and Applications, Springer, vol. 58(1), pages 31-85, May.
    4. Richard Pierse, 2006. "Optimal control in nonlinear models: a generalised Gauss-Newton algorithm with analytic derivatives," School of Economics Discussion Papers 0906, School of Economics, University of Surrey.
    5. Andrew Patton, 2002. "(IAM Series No 001) On the Out-Of-Sample Importance of Skewness and Asymetric Dependence for Asset Allocation," FMG Discussion Papers dp431, Financial Markets Group.
    6. Francisco Gallego & Andrés Hernando, 2009. "School Choice in Chile: Looking at the Demand Side," Documentos de Trabajo 356, Instituto de Economia. Pontificia Universidad Católica de Chile..
    7. Claude Hillinger, 2002. "A General Theory of Price and Quantity Aggregation and Welfare Measurement," CESifo Working Paper Series 818, CESifo.
    8. Salerno, Gillian & Beard, Rodney & McDonald, Stuart, 2007. "Rent Seeking Behavior and Optimal Taxation of Pollution in Shallow Lakes," MPRA Paper 11225, University Library of Munich, Germany, revised 22 Oct 2008.
    9. Maria Casanova-Rivas, 2008. "Dynamic Complementarities: A Computational and Empirical Analysis of Couples' Retirement Decisions," 2008 Meeting Papers 1073, Society for Economic Dynamics.
    10. Heer, Burkhard & Polito, Vito & Wickens, Michael R., 2020. "Population aging, social security and fiscal limits," Journal of Economic Dynamics and Control, Elsevier, vol. 116(C).
    11. Andreas Lanz & Gregor Reich & Ole Wilms, 2022. "Adaptive grids for the estimation of dynamic models," Quantitative Marketing and Economics (QME), Springer, vol. 20(2), pages 179-238, June.
    12. Jacques Le Cacheux & Vincent Touzé, 2002. "Les modèles d'équilibre général calculable à générations imbriquées. Enjeux, méthodes et résultats," Revue de l'OFCE, Presses de Sciences-Po, vol. 80(1), pages 87-113.
    13. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    14. Pelin Ilbas, 2006. "Optimal Monetary Policy rules for the Euro area in a DSGE framework," Working Papers of Department of Economics, Leuven ces0613, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    15. Atanas Christev, 2006. "Learning Hyperinflations," Computing in Economics and Finance 2006 475, Society for Computational Economics.
    16. Kollmann, Robert, 2003. "Monetary Policy Rules in an Interdependent World," CEPR Discussion Papers 4012, C.E.P.R. Discussion Papers.
    17. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    18. Frölich, Markus & Lechner, Michael, 2010. "Exploiting Regional Treatment Intensity for the Evaluation of Labor Market Policies," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1014-1029.
    19. Nikolaj Malchow-Møller & Michael Svarer, 2003. "Estimation of the multinomial logit model with random effects," Applied Economics Letters, Taylor & Francis Journals, vol. 10(7), pages 389-392.
    20. Röhrs, Sigrid & Winter, Christoph, 2017. "Reducing government debt in the presence of inequality," Journal of Economic Dynamics and Control, Elsevier, vol. 82(C), pages 1-20.

    More about this item

    Keywords

    Deterministic control systems; Dynamic Programming; equilibrium point; Euler¡¯s equation; stability;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:1:p:115. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.