Optimal Stopping and the Sufficiency of Randomized Threshold Strategies
Probability
2017-08-04 v1
Abstract
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which the value associated to a stopping rule depends on the law of the stopped process. If this value is quasi-convex on the space of attainable laws then it is a well known result that it is sufficient to restrict attention to the class of threshold strategies. However, if the objective function is not quasi-convex, this may not be the case. We show that, nonetheless, it is sufficient to restrict attention to mixtures of threshold strategies.
Keywords
Cite
@article{arxiv.1708.01038,
title = {Optimal Stopping and the Sufficiency of Randomized Threshold Strategies},
author = {Vicky Henderson and David Hobson and Matthew Zeng},
journal= {arXiv preprint arXiv:1708.01038},
year = {2017}
}