Book review:                   

By Andreas Kyprianou

Published in :      International Statistics Institute Book Reviews 

Rama Cont and Peter Tankov
Financial Modelling with Jump Processes
Chapman & Hall, 2004
                                                                                                                                                              
Contents:
                                                                                                                                                              
1. Financial modelling beyond Brownian motion.
2. Basic tools .
3. L\'evy processes: Definitions and properties.
4. Building L\'evy processes.
5. Multidimensional models with jumps.
6. Simulating L\'evy processes.
7. Modelling financial time series with L\'evy processes.
8. Stochastic calculus for jump processes.
9. Measure transformations for L\'evy processes.
10. Pricing and hedging in incomplete markets.
11. Risk-neutral modelling with exponential L\'evy processes.
12. Integro-differential equation and numerical methods.
13. Inverse problems and model calibration.
14. Time inhomogenous jump processes.
15. Stochastic volatility models with jumps.
                                                                                                                                                              
Readership: Graduate students and researchers working in financial mathematics as well as the modern army of highly educated mathematicians
working in banks and financial institutions.
                                                                                                                                                              
This book is an extremely rich source of information for recent developments in the use of jump processes in financial modelling, in
particular the use of L\'evy processes. The contents list speaks for itself in this respect. The book as a whole is non-assuming in the sense
that the mathematical and financial background the reader would seem to need is little more than what one would expect from a
masters level education from any good European mathematics department offering courses in financial stochastics.  The authors work at a
comfortable mathematical pace choosing carefully which proofs to include and exclude and never losing sight of financial interpretation and
application. The book comes with many additional perks. For example, many examples and local summaries, a balanced perspective on the shortfalls of
the theory being presented, making the effort to show how standard results and and expressions for semi-martingales look like for L\'evy processes
and clear referencing for further reading. The book is also spiced with some very interesting historical notes about prominent (French)
mathematicians whose work has ultimately contributed to the foundations of financial stochastics.
                                                                                                                                                              
The authors conclude the main body of their text by saying: "We hope that the present volume will encourage more researchers and practitioners to
contribute to this topic and improve on our understanding of theoretical, numerical and practical issues related to financial modelling with jump
processes". I am quite convinced that this goal will be achieved.