ABSTRACT
Lorsque l’on expose devant un public de mathématiciens […] on peut supposer que chacun connait les variétés de Stein ou les nombres de Betti d’un espace topologique; mais si l’on a besoin d’une intégrale stochastique, on doit définir à partir de zéro les filtrations, les processus prévisibles, les martingales, etc. Il y a là quelque chose d’anormal. Les raisons en sont bien sûr nombreuses, à commencer par le vocabulaire esotérique des probabilistes…
Laurent Schwartz
Modern probability theory has become the natural language for formulating quantitative models of financial markets. This chapter presents, in the form of a crash course, some of its tools and concepts that will be important in the sequel. Although the reader is assumed to have some background knowledge on random variables and probability, there are some tricky notions that we have found useful to recall. Instead of giving a catalog of definitions and theorems, which can be found elsewhere, we have tried to justify why these definitions are relevant and to promote an intuitive understanding of the main results.
