ABSTRACT
Recall that in (7.1) we left our good friend Ann in a gambling house with the problem of finding the best possible time to stop gambling. In this chapter, I shall give several solutions to Ann’s problem, and I shall find the optimal stopping strategies for various games. The main tool will be the theory of martingales as developed in Chapter 7. However, I shall not assume that the fortune of Ann after the n th game is a submartingale or supermartingale, but rather construct a suitable martingale on which the results of Chapter 7 may be applied. This construction will be the objective of this section.
