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Robust Statistic Estimation in Constrained Optimal Control Problems of Pollution Accumulation (Part II: Markovian Switchings)

Author

Listed:
  • Beatris Adriana Escobedo-Trujillo

    (Facultad de Ingeniería, Universidad Veracruzana, Coatzacoalcos 96535, Mexico)

  • José Daniel López-Barrientos

    (Facultad de Ciencias Actuariales, Universidad Anáhuac Mexico, Naucalpan de Juárez 52786, Mexico)

  • Carmen Geraldi Higuera-Chan

    (Departamento de Matemáticas, Universidad de Sonora, Hermosillo 83000, Mexico)

  • Francisco Alejandro Alaffita-Hernández

    (Centro de Investigación en Recursos Energéticos y Sustentables, Universidad Veracruzana, Coatzacoalcos 96535, Mexico)

Abstract

This piece is a follow-up of the research started by the authors on the constrained optimal control problem applied to pollution accumulation. We consider a dynamic system governed by a diffusion process with multiple modes that depends on an unknown parameter. We will study the components of the model and their restrictions and propose a scheme to solve the problem in which it is possible to determine (adaptive) policies that maximize a suitable discounted reward criterion using standard dynamic programming techniques in combination with discrete estimation methods for the unknown parameter. Finally, we develop a numerical example to illustrate our results with a particular case of the method of minimum least square error approximation.

Suggested Citation

  • Beatris Adriana Escobedo-Trujillo & José Daniel López-Barrientos & Carmen Geraldi Higuera-Chan & Francisco Alejandro Alaffita-Hernández, 2023. "Robust Statistic Estimation in Constrained Optimal Control Problems of Pollution Accumulation (Part II: Markovian Switchings)," Mathematics, MDPI, vol. 11(4), pages 1-22, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1045-:d:1072973
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    References listed on IDEAS

    as
    1. Kawaguchi, Kazuhito & Morimoto, Hiroaki, 2007. "Long-run average welfare in a pollution accumulation model," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 703-720, February.
    2. Beatris A. Escobedo-Trujillo & Carmen G. Higuera-Chan & José Daniel López-Barrientos, 2021. "Controlled Switching Diffusions Under Ambiguity: The Average Criterion," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 1-26, December.
    3. Nadine Hilgert & J. Minjárez-Sosa, 2006. "Adaptive control of stochastic systems with unknown disturbance distribution: discounted criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 443-460, July.
    4. Beatris Adriana Escobedo-Trujillo & José Daniel López-Barrientos & Javier Garrido-Meléndez, 2021. "A Constrained Markovian Diffusion Model for Controlling the Pollution Accumulation," Mathematics, MDPI, vol. 9(13), pages 1-29, June.
    5. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
    6. José López-Barrientos & Héctor Jasso-Fuentes & Beatris Escobedo-Trujillo, 2015. "Discounted robust control for Markov diffusion processes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 53-76, April.
    7. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 335-338, July.
    8. Shoji, Isao, 1997. "A note on asymptotic properties of the estimator derived from the Euler method for diffusion processes at discrete times," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 153-159, December.
    9. Louis Anthony (Tony) Cox, 2012. "Confronting Deep Uncertainties in Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 32(10), pages 1607-1629, October.
    10. Beatris Adriana Escobedo-Trujillo & José Daniel López-Barrientos & Carmen Geraldi Higuera-Chan & Francisco Alejandro Alaffita-Hernández, 2023. "Robust Statistic Estimation of Constrained Optimal Control Problems of Pollution Accumulation (Part I)," Mathematics, MDPI, vol. 11(4), pages 1-19, February.
    11. Morimoto,Hiroaki, 2010. "Stochastic Control and Mathematical Modeling," Cambridge Books, Cambridge University Press, number 9780521195034.
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