Problems and Solutions in Mathematical Finance: Stochastic Calculus, Volume I

Preface

Mathematical finance is based on highly rigorous and, on occasions, abstract mathematical structures that need to be mastered by anyone who wants to be successful in this field, be it working as a quant in a trading environment or as an academic researcher in the field. It may appear strange, but it is true, that mathematical finance has turned into one of the most advanced and sophisticated field in applied mathematics. This development has had considerable impact on financial engineering with its extensive applications to the pricing of contingent claims and synthetic cash flows as analysed both within financial institutions (investment banks) and corporations. Successful understanding and application of financial engineering techniques to highly relevant and practical situations requires the mastering of basic financial mathematics. It is precisely for this purpose that this book series has been written.

In Volume I, the first of a four volume work, we develop briefly all the major mathematical concepts and theorems required for modern mathematical finance. The text starts with probability theory and works across stochastic processes, with main focus on Wiener and Poisson processes. It then moves to stochastic differential equations including change of measure and martingale representation theorems. However, the main focus of the book remains practical. After being introduced to the fundamental concepts the reader is invited to test his/her knowledge on a whole range ...