Multiple optimal stopping rules and their applications

Abstract: 

We observe a sequence of random variables and have to decide when we must stop, given that there is no recall allowed, that is, a random variable once rejected cannot be chosen later on. Our decision to stop depends on the observations already made, but does not depend on the future which is not yet known. The objective is to find an optimal procedure that maximizes an expected reward. We consider problems when at least two stops are required, for example, a sequential problem of selling several identical assets over a finite time horizon.