This book is a comprehensive, self-contained, and unified treatment of the main theory and application of mathematical methods behind modern-day financial mathematics.

Giuseppe Campolieti is Professor of Mathematics at Wilfrid Laurier University in Waterloo, Canada. He has been Natural Sciences and Engineering Research Council postdoctoral research fellow and university research fellow at the University of Toronto. In 1998, he joined the Masters in Mathematical Finance as an instructor and later as an adjunct professor in financial mathematics until 2002. Dr. Campolieti also founded a financial software and consulting company in 1998. He joined Laurier in 2002 as Associate Professor of Mathematics and as SHARCNET Chair in Financial Mathematics.

Roman N. Makarov is Associate Professor and Chair of Mathematics at Wilfrid Laurier University. Prior to joining Laurier in 2003, he was an Assistant Professor of Mathematics at Siberian State University of Telecommunications and Informatics and a senior research fellow at the Laboratory of Monte Carlo Methods at the Institute of Computational Mathematics and Mathematical Geophysics in Novosibirsk, Russia.

List of Figures and Tables

Preface

I Introduction to Pricing and Management of Financial Securities

1 Mathematics of Compounding
2 Primer on Pricing Risky Securities

3 Portfolio Management

4 Primer on Derivative Securities

II Discrete-Time Modelling

5 Single-Period Arrow-Debreu Models

6 Introduction to Discrete-Time Stochastic Calculus

7 Replication and Pricing in the Binomial Tree Model

8 General Multi-Asset Multi-Period Model

Appendices

A Elementary Probability Theory

B Glossary of Symbols and Abbreviations

C Answers and Hints to Exercises

References

Index