Controlled Semi-Markov Chains with Risk-Sensitive Average Cost Criterion

Selene Chávez-Rodríguez (), Rolando Cavazos-Cadena () and Hugo Cruz-Suárez ()
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Selene Chávez-Rodríguez: Benemérita Universidad Autónoma de Puebla
Rolando Cavazos-Cadena: Universidad Autónoma Agraria Antonio Narro
Hugo Cruz-Suárez: Benemérita Universidad Autónoma de Puebla

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 2, No 18, 670-686

Abstract: Abstract This work concerns with semi-Markov decision chains on a finite state space. Assuming that the controller has a constant and positive risk-sensitive coefficient, an optimality equation for the corresponding (long-run) risk-sensitive average cost index is formulated and, under suitable continuity-compactness conditions, it is shown that a solution of such an equation determines the optimal average cost, as well as an optimal stationary policy. Additionally, if the underlying Markov chain is communicating, then it is proved that the optimality equation has a solution.

Keywords: Exponential utility; Certainty equivalent; Light tails; Communicating underlying chain; Risk-sensitive control; 90C40; 93E20; 60J05 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-016-0916-z

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