ABSTRACT

The first two chapters of this book dealt with discrete-time models. We had the opportunity to see the importance of the concepts of martingales, selffinancing strategy and the Snell envelope. In this chapter, we are going to elaborate on these ideas in a continuous-time framework. In particular, we shall introduce the mathematical tools needed to model financial assets and to price options. In continuous-time, the technical aspects are more advanced and more difficult to handle than in discrete-time, but the main ideas are fundamentally the same.