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A Constrained Markovian Diffusion Model for Controlling the Pollution Accumulation

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  • Beatris Adriana Escobedo-Trujillo

    (Facultad de Ingeniería, Universidad Veracruzana, Xalapa de Enriquez 91090, Mexico
    These authors contributed equally to this work.)

  • José Daniel López-Barrientos

    (Facultad de Ciencias Actuariales, Universidad Anáhuac México, Naucalpan de Juárez 52786, Mexico
    These authors contributed equally to this work.)

  • Javier Garrido-Meléndez

    (Facultad de Ingeniería, Universidad Veracruzana, Xalapa de Enriquez 91090, Mexico)

Abstract

This work presents a study of a finite-time horizon stochastic control problem with restrictions on both the reward and the cost functions. To this end, it uses standard dynamic programming techniques, and an extension of the classic Lagrange multipliers approach. The coefficients considered here are supposed to be unbounded, and the obtained strategies are of non-stationary closed-loop type. The driving thread of the paper is a sequence of examples on a pollution accumulation model, which is used for the purpose of showing three algorithms for the purpose of replicating the results. There, the reader can find a result on the interchangeability of limits in a Dirichlet problem.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1466-:d:580023
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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. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," The Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
    3. Morimoto,Hiroaki, 2010. "Stochastic Control and Mathematical Modeling," Cambridge Books, Cambridge University Press, number 9780521195034, November.
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    Cited by:

    1. 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.
    2. 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.

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