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

Beatris Adriana Escobedo-Trujillo, José Daniel López-Barrientos (), Carmen Geraldi Higuera-Chan and Francisco Alejandro Alaffita-Hernández
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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

Mathematics, 2023, vol. 11, issue 4, 1-22

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.

Keywords: consistent estimators; multiple Markovian modes; discounted cost; maximum likelihood estimators; least square errors (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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