Existence of Risk-Sensitive Optimal Stationary Policies for Controlled Markov Processes

Journal Article · Mon Nov 15 00:00:00 EST 1999 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S002459900126· OSTI ID:21067539

Hernandez-Hernandez, D

In this paper we are concerned with the existence of optimal stationary policies for infinite-horizon risk-sensitive Markov control processes with denumerable state space, unbounded cost function, and long-run average cost. Introducing a discounted cost dynamic game, we prove that its value function satisfies an Isaacs equation, and its relationship with the risk-sensitive control problem is studied. Using the vanishing discount approach, we prove that the risk-sensitive dynamic programming inequality holds, and derive an optimal stationary policy.

• OSTI ID: 21067539
• Journal Information: Applied Mathematics and Optimization, Vol. 40, Issue 3; Other Information: DOI: 10.1007/s002459900126; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONTROL THEORY
COST
DYNAMIC PROGRAMMING
EQUATIONS
FUNCTIONS
GAME THEORY
HAZARDS
MARKOV PROCESS
MATHEMATICAL SPACE