2017/08/03 by Vicky Henderson, David Hobson, Henderson, Vicky +3
Mathematics · #60G40 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G40
paper · pdf · doi:10.48550/arxiv.1708.01038
arxiv created 2017/08/03 · arxiv updated 2017/08/04
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.