2017/08/03 by Henderson, Vicky, Hobson, David, Zeng, Matthew
#60G40 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1708.01038
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.