Multiobjective Stopping Problem for Discrete-Time Markov Processes: Convex Analytic Approach
Multiobjective Stopping Problem for Discrete-Time Markov Processes: Convex Analytic Approach
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DOI：
10.1239/jap/1294170511
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发表时间：
2010-12
影响因子：
1
通讯作者：
François Dufour;A. Piunovskiy
中科院分区：
文献类型：
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作者：
François Dufour;A. Piunovskiy
本文利用凸分析方法研究了具有一般状态空间的马氏链的带约束的最优停止问题。假设成本是非负的。我们的模型不假定是暂态的或吸收的，并且停止时间不一定有一个有限的期望。因此，占用度量不一定是有限的，这给相关线性规划的分析带来了一些困难。在一个很弱的假设下，证明了线性问题存在最优解，从而保证了带约束的最优停止问题的最优停止策略的存在性。
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.