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Controlled Switching Diffusions Under Ambiguity: The Average Criterion

Author

Listed:
  • Beatris A. Escobedo-Trujillo

    (Facultad de Ingeniería, Universidad Veracruzana, Campus Coatzacoalcos. Av. Universidad km 7.5 col. Santa Isabel, CP96535, Coatzacoalcos, Veracruz, México)

  • Carmen G. Higuera-Chan

    (Departamento de Matemáticas, Universidad de Sonora, Rosales s/n, Col. Centro 83000 Hermosillo, Sonora, México)

  • José Daniel López-Barrientos

    (Facultad de Ciencias Actuariales, Universidad Anáhuac México, Av. Universidad Anáhuac, no. 46 Col. Lomas Anáhuac, Huixquilucan, Edo. de México, México)

Abstract

This paper concerns controlled switching diffusions. In particular, we consider that the drift coefficient of the diffusion process depends on an unknown (and possibly nonobservable) parameter. For giving solution to our control problem, we formulate it as a game against nature, where the ambiguity is represented by nature that chooses values of the unknown parameter through actions so playing the role as an opposite player of the controller. Our objective is to give conditions to characterize the ergodic optimality and guarantee the existence of optimal policies for the central controller. Finally, we provide two examples to illustrate our results.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:23:y:2021:i:04:n:s0219198921500171
    DOI: 10.1142/S0219198921500171
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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.

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