Tools from Stochastic Analysis for Mathematical Finance : A Gentle Introduction

The idea of this document is to provide the reader with an intuitive, yet rigorous and comprehensive introduction to the main tools in stochastic analysis required in Finance to understand the modern modelling, pricing and hedging techniques. The most important models (Brownian motion, arithmetic and geometric Brownian motion, mean-reverting models, stochastic and jump processes) are considered and their properties illustrated with the help of Matlab codes and videos. We would like to emphasize that this document is very much work in progress and we would like to encourage readers to get in touch with us with feedback, comments, suggestions for additions and, of course, corrections of typos. All of these will be gratefully acknowledged in the future releases of this document