ABSTRACT

The purpose of this chapter is to address the pricing and hedging of American options and to establish the link between these questions and the optimal stopping problem. To do so, we will need to define the notion of stopping time, which will enable us to model exercise strategies for American options. We will also define the Snell envelope, which is the fundamental concept used to solve the optimal stopping problem. The application of these concepts to American options will be described in Section 2.5.