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Discounted robust control for Markov diffusion processes

Author

Listed:
  • José López-Barrientos
  • Héctor Jasso-Fuentes
  • Beatris Escobedo-Trujillo

Abstract

In this paper we give conditions for the existence of discounted robust optimal policies under an infinite planning horizon for a general class of controlled diffusion processes. As for the attribute “robust” we mean the coexistence of unknown and non-observable parameters affecting the coefficients of the diffusion process. To obtain optimality, we rewrite the problem as a zero-sum game against nature, also known as worst case optimal control. Our analysis is based on the use of the dynamic programming technique by showing, among other facts, the existence of classical solutions (twice differentiable solutions) of the so-called Hamilton Jacobi Bellman equation. We provide an example on pollution accumulation control to illustrate our results. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:23:y:2015:i:1:p:53-76
    DOI: 10.1007/s11750-014-0323-2
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    References listed on IDEAS

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    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. Alexander Schied, 2008. "Robust optimal control for a consumption-investment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 1-20, February.
    3. Arie Hordijk & Olaf Passchier & Floske Spieksma, 1997. "Optimal service control against worst case admission policies: A multichained stochastic game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(2), pages 281-301, June.
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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. Dariusz Zawisza, 2016. "Smooth solutions to discounted reward control problems with unbounded discount rate and financial applications," Papers 1602.00899, arXiv.org, revised Feb 2016.
    3. José Daniel López-Barrientos & Ekaterina Viktorovna Gromova & Ekaterina Sergeevna Miroshnichenko, 2020. "Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
    4. 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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