Probability Theory and Stochastic Processes

This book is an extension of Probability for Finance to multi-period financial models, either in the discrete or continuous-time framework. It describes the most important stochastic processes used in finance in a pedagogical way, especially Markov chains, Brownian motion and martingales. It also shows how mathematical tools like filtrations, Ito's lemma or Girsanov theorem should be understood in the framework of financial models. It also provides many illustrations coming from the financial literature.

This book provides technical support for students in finance. It reviews the main probabilistic tools used in financial models in a pedagogical way, starting from simple concepts like random variables and tribes and going to more sophisticated ones like conditional expectations and limit theorems. Many illustrations are given, taken from the financial literature. The book is also a prerequisite for Stochastic Processes for Finance published in the same collection.