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2001 | 28 | 1 | 93-109
Tytuł artykułu

Stationary optimal policies in a class of multichain positive dynamic programs with finite state space and risk-sensitive criterion

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This work concerns Markov decision processes with finite state space and compact action sets. The decision maker is supposed to have a constant-risk sensitivity coefficient, and a control policy is graded via the risk-sensitive expected total-reward criterion associated with nonnegative one-step rewards. Assuming that the optimal value function is finite, under mild continuity and compactness restrictions the following result is established: If the number of ergodic classes when a stationary policy is used to drive the system depends continuously on the policy employed, then there exists an optimal stationary policy, extending results obtained by Schal (1984) for risk-neutral dynamic programming. We use results recently established for unichain systems, and analyze the general multichain case via a reduction to a model with the unichain property.
Słowa kluczowe
  • Departamento de Estadistica y Calculo, Universidad Autonoma Agraria Antonio Narro, Buenavista, Saltillo COAH 25315, Mexico
  • Departamento de Matematicas, Universidad Autonoma Metropolitana, Campus Iztapalapa, Avenida Michoacan y La Purisima s/n, Col. Vicentina, Mexico D.F. 09340, Mexico
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