# Optimal stationary policies inrisk-sensitive dynamic programs with finite state spaceand nonnegative rewards

Rolando Cavazos-Cadena; Raúl Montes-de-Oca

Applicationes Mathematicae (2000)

- Volume: 27, Issue: 2, page 167-185
- ISSN: 1233-7234

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topCavazos-Cadena, Rolando, and Montes-de-Oca, Raúl. "Optimal stationary policies inrisk-sensitive dynamic programs with finite state spaceand nonnegative rewards." Applicationes Mathematicae 27.2 (2000): 167-185. <http://eudml.org/doc/219265>.

@article{Cavazos2000,

abstract = {This work concerns controlled Markov chains with finite state space and nonnegative rewards; it is assumed that the controller has a constant risk-sensitivity, and that the performance ofa control policy is measured by a risk-sensitive expected total-reward criterion. The existence of optimal stationary policies isstudied within this context, and the main resultestablishes the optimalityof a stationary policy achieving the supremum in the correspondingoptimality equation, whenever the associated Markov chain hasa unique positive recurrent class. Two explicit examples are providedto show that, if such an additional condition fails, an optimal stationarypolicy cannot be generally guaranteed. The results of this note, which consider both the risk-seeking and the risk-averse cases, answer an extended version of a question recently posed in Puterman (1994).},

author = {Cavazos-Cadena, Rolando, Montes-de-Oca, Raúl},

journal = {Applicationes Mathematicae},

keywords = {unichain property; Markov decision processes; risk-sensitive optimality equation; risk-sensitive expected total- reward criterion},

language = {eng},

number = {2},

pages = {167-185},

title = {Optimal stationary policies inrisk-sensitive dynamic programs with finite state spaceand nonnegative rewards},

url = {http://eudml.org/doc/219265},

volume = {27},

year = {2000},

}

TY - JOUR

AU - Cavazos-Cadena, Rolando

AU - Montes-de-Oca, Raúl

TI - Optimal stationary policies inrisk-sensitive dynamic programs with finite state spaceand nonnegative rewards

JO - Applicationes Mathematicae

PY - 2000

VL - 27

IS - 2

SP - 167

EP - 185

AB - This work concerns controlled Markov chains with finite state space and nonnegative rewards; it is assumed that the controller has a constant risk-sensitivity, and that the performance ofa control policy is measured by a risk-sensitive expected total-reward criterion. The existence of optimal stationary policies isstudied within this context, and the main resultestablishes the optimalityof a stationary policy achieving the supremum in the correspondingoptimality equation, whenever the associated Markov chain hasa unique positive recurrent class. Two explicit examples are providedto show that, if such an additional condition fails, an optimal stationarypolicy cannot be generally guaranteed. The results of this note, which consider both the risk-seeking and the risk-averse cases, answer an extended version of a question recently posed in Puterman (1994).

LA - eng

KW - unichain property; Markov decision processes; risk-sensitive optimality equation; risk-sensitive expected total- reward criterion

UR - http://eudml.org/doc/219265

ER -

## References

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- R. Cavazos-Cadena and R. Montes-de-Oca (1999), Optimal stationarypolicies in controlled Markov chains with theexpected total-reward criterion, Research Report No. 1.01.010.99, Univ. Autónoma Metropolitana, Campus Iztapalapa, México, D.F. Zbl0937.90114
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