PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2000 | 27 | 2 | 167-185
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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).
Rocznik
Tom
27
Numer
2
Strony
167-185
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-04-20
poprawiono
1999-10-05
Twórcy
  • Departamento de Estadísticay Cálculo, Universidad Autónoma Agraria Antonio Narro, Buenavista, Saltillo COAH 25315, México
  • Departamento de Matemáticas, Universidad Autónoma Metropolitana, Campus Iztapalapa, Avenida Michoacán y La Purísima s/n, Col. Vicentina, México, D.F. 09340, México
Bibliografia
  • M. G. Ávila-Godoy (1998), Controlled Markov chains with exponentialrisk-sensitive criteria: modularity, structured policies and applications, Ph.D. Dissertation, Dept. of Math., Univ. ofArizona, Tucson, AZ.
  • R. Cavazos-Cadena and E. Fernández-Gaucherand (1999), Controlled Markov chains with risk-sensitive criteria:average cost, optimality equations, and optimal solutions, Math. Methods Oper. Res. 43, 121-139.
  • 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.
  • P. C. Fishburn (1970), Utility Theory for Decision Making, Wiley, New York.
  • W. H. Fleming and D. Hernández-Hernández (1997), Risk-sensitive control of finite machines on an infinite horizon I, SIAM J. Control Optim. 35, 1790-1810.
  • O. Hernández-Lerma (1989), Adaptive Markov Control Processes, Springer, New York.
  • K. Hinderer (1970), Foundations of Non-Stationary Dynamic Programming with Discrete Time Parameter, Lecture Notes in Oper. Res. 33, Springer, New York.
  • R. A. Howard and J. E. Matheson (1972), Risk-sensitive Markov decisionprocesses, Management Sci. 18, 356-369.
  • M. Loève (1977), Probability Theory I, 4th ed., Springer, New York.
  • J. W. Pratt (1964), Risk aversion in the small and in the large, Econometrica 32, 122-136.
  • M. L. Puterman (1994), Markov Decision Processes, Wiley, New York.
  • S. M. Ross (1970), Applied Probability Models with Optimization Applications, Holden-Day, San Francisco.
  • R. Strauch (1966), Negative dynamic programming, Ann.Math. Statist. 37, 871-890.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv27i2p167bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.