Multiobjective Stopping Problem for Discrete-Time Markov Processes: Convex Analytic Approach

The purpose of this paper is to study an optimal stopping problem with constraints for a Markov chain with general state space by using the convex analytic approach. The costs are assumed to be nonnegative. Our model is not assumed to be transient or absorbing and the stopping time does not necessar...

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Bibliographic Details
Published in:Journal of applied probability 2010-12, Vol.47 (4), p.947-966
Main Authors: Dufour, F., Piunovskiy, A. B.
Format: Article
Language:English
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Summary:The purpose of this paper is to study an optimal stopping problem with constraints for a Markov chain with general state space by using the convex analytic approach. The costs are assumed to be nonnegative. Our model is not assumed to be transient or absorbing and the stopping time does not necessarily have a finite expectation. As a consequence, the occupation measure is not necessarily finite, which poses some difficulties in the analysis of the associated linear program. Under a very weak hypothesis, it is shown that the linear problem admits an optimal solution, guaranteeing the existence of an optimal stopping strategy for the optimal stopping problem with constraints.
ISSN:0021-9002
1475-6072
DOI:10.1017/S0021900200007282