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Vanishing discount approximations in controlled Markov chains with risk-sensitive average criterion

Published online by Cambridge University Press:  20 March 2018

Rolando Cavazos-Cadena  and
Daniel Hernández-Hernández
Rolando Cavazos-Cadena*
Affiliation:
Universidad Autónoma Agraria Antonio Narro
Daniel Hernández-Hernández*
Affiliation:
Centro de Investigación en Matemáticas
*
* Postal address: Departamento de Estadística y Cálculo, Universidad Autónoma Agraria Antonio Narro, Boulevard Antonio Narro 1923, Buenavista, Saltillo, Coah, 25315, México.
** Postal address: Centro de Investigación en Matemáticas, Apartado Postal 402, Guanajuato, Gto, 36000, México. Email address: dher@cimat.mx
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Abstract

This work concerns Markov decision chains on a finite state space. The decision-maker has a constant and nonnull risk sensitivity coefficient, and the performance of a control policy is measured by two different indices, namely, the discounted and average criteria. Motivated by well-known results for the risk-neutral case, the problem of approximating the optimal risk-sensitive average cost in terms of the optimal risk-sensitive discounted value functions is addressed. Under suitable communication assumptions, it is shown that, as the discount factor increases to 1, appropriate normalizations of the optimal discounted value functions converge to the optimal average cost, and to the functional part of the solution of the risk-sensitive average cost optimality equation.

Keywords

Exponential utilitycertainty equivalentvanishing discount methodHölder's inequalityconvex function

MSC classification

Secondary: 90C39: Dynamic programming
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue 1 , March 2018 , pp. 204 - 230
Copyright
Copyright © Applied Probability Trust 2018 

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