On singular control problems, the time-stretching method, and the weak-M1 topology

Asaf Cohen

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arXiv · 1905.02608

On singular control problems, the time-stretching method, and the weak-M1 topology

Asaf Cohen

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Abstract

We consider a general class of singular control problems with state constraints. Budhiraja and Ross (2006) established the existence of optimal controls for a relaxed version of this class of problems by using the so-called `time-stretching' method and the J1-topology. We show that the weak-M1 topology is better suited for establishing existence, since it allows to bypass the time-transformations, without any additional effort. Furthermore, we reveal how the time-scaling feature in the definition of the weak-M1 distance embeds the time-stretching method's scheme. This case study suggests that one can benefit from working with the weak-M1 topology in other singular control frameworks, such as queueing control problems under heavy traffic.

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Asaf Cohen. 2019-05-07. On singular control problems, the time-stretching method, and the weak-M1 topology. https://arxiv.org/abs/1905.02608

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