Constrained Markov control processes with randomized discounted cost criteria: Occupation measures and extremal points

Article type: Research Article

Authors: González-Hernández, Juan | López-Martínez, Raquiel R. | Minjárez-Sosa, J. Adolfo^; | Gabriel-Arguelles, J. Rigoberto

Affiliations: Departamento de Probabilidad y Estadística, IIMAS-UNAM, México DF, Mexico | Facultad de Matemáticas, Universidad Veracruzana, Xalapa Ver., Mexico | Departamento de Matemáticas, Universidad de Sonora, Rosales s/n, Centro, Hermosillo, Sonora, Mexico | Facultad de Matemáticas, Universidad Veracruzana, Xalapa Ver., Mexico

Note: [] Corresponding author: J. Adolfo Minjárez-Sosa, Departamento de Matemáticas, Universidad de Sonora, Rosales s/n, Centro, 83000 Hermosillo, Sonora, Mexico. E-mail: aminjare@gauss.mat.uson.mx

Abstract: In this paper we study constrained Markov control processes on Borel spaces with possibly unbounded costs, under a discounted optimality criterion with random discount factor and restrictions of the same kind. Imposing mild conditions, we show the solubility of the corresponding control problem. Furthermore, we characterize the corresponding occupation measures and show the existence of randomized optimal control policies. These optimal strategies are convex combinations of deterministic stationary policies.

Keywords: Constrained discounted cost, random discount factor, occupation measures, direct method

DOI: 10.3233/RDA-2012-0063

Journal: Risk and Decision Analysis, vol. 4, no. 3, pp. 163-176, 2013