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

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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
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    References listed on IDEAS

    as
    1. Fuente,Angel de la, 2000. "Mathematical Methods and Models for Economists," Cambridge Books, Cambridge University Press, number 9780521585293, September.
    2. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    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)

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    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

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