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**Monte Carlo methods in financial engineering.**
*(English)*
Zbl 1038.91045

Applications of Mathematics 53. New York, NY: Springer (ISBN 0-387-00451-3/hbk). xiii, 596 p. (2004).

This recent book is a valuable addition to the references devoted to Monte Carlo methods. It is an outgrowth of lecture notes the author has used over several years at different universities and is intended to serve graduate students in financial engineering, researchers interested in the application of Monte Carlo methods in finance, and practitioners implementing models in industry. Despite the fact that the audience comes from different fields of activity and with different prerequisites, the author succeeded in choosing the most actual topics in financial engineering and in presenting them in an appropriate way by keeping a suitable balance between mathematical rigour and an audience friendly language.

The text is divided into nine chapters. In essence, Chapters 1 to 3 are concerned with running simulations whereas Chapters 4 to 6 deal with ways of running them better. Chapters 7 to 9 address topics specific to the application of Monte Carlo methods in finance. To help the reader, three appendices provide basic results on convergence concepts, stochastic calculus, and the term structure of interest rates. A large bibliography of 358 entries accompanies this text.

In short, the reader will find this book extremely lucid and useful.

Contents: Foundations, Generating random numbers and random variables, Generating sample paths, Variance reduction techniques, Quasi-Monte Carlo, Discretization methods, Estimating sensitivities, Pricing American options, Applications in risk management.

The text is divided into nine chapters. In essence, Chapters 1 to 3 are concerned with running simulations whereas Chapters 4 to 6 deal with ways of running them better. Chapters 7 to 9 address topics specific to the application of Monte Carlo methods in finance. To help the reader, three appendices provide basic results on convergence concepts, stochastic calculus, and the term structure of interest rates. A large bibliography of 358 entries accompanies this text.

In short, the reader will find this book extremely lucid and useful.

Contents: Foundations, Generating random numbers and random variables, Generating sample paths, Variance reduction techniques, Quasi-Monte Carlo, Discretization methods, Estimating sensitivities, Pricing American options, Applications in risk management.

Reviewer: Radu Theodorescu (Quebec)

### MSC:

91-02 | Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance |

91G60 | Numerical methods (including Monte Carlo methods) |

65C05 | Monte Carlo methods |

65C10 | Random number generation in numerical analysis |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

91B62 | Economic growth models |

91B70 | Stochastic models in economics |