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**Fundamentals of actuarial mathematics.**
*(English)*
Zbl 1100.62095

Hoboken, NJ: John Wiley & Sons (ISBN 0-470-01689-2/hbk). xix, 372 p. (2006).

This well written book is a welcome addition to the actuarial literature. It covers two important areas in actuarial science: life contingencies and risk theory, including basics of ruin theory. It has twenty chapters and an appendix that reviews probability theory. Life contingencies are treated in the first sixteen chapters, which are divided into two parts, deterministic and stochastic models. The mathematics prerequisites are undergraduate level calculus, linear algebra and probability theory. Exercises are given at the end of each chapter.

Unlike many other books on life contingencies, this book uses vector notation quite extensively. It employs symbols that are not part of the system of classical actuarial notation. It has, however, included the standard notation in separate sections at the end of the relevant chapters. Another distinct feature of the book is the use of Excel spreadsheet calculations. The book covers the current syllabus of the Society of Actuaries examination on life contingencies. However, because of notational differences, this is not an efficient book for students to prepare for the examination.

Unlike many other books on life contingencies, this book uses vector notation quite extensively. It employs symbols that are not part of the system of classical actuarial notation. It has, however, included the standard notation in separate sections at the end of the relevant chapters. Another distinct feature of the book is the use of Excel spreadsheet calculations. The book covers the current syllabus of the Society of Actuaries examination on life contingencies. However, because of notational differences, this is not an efficient book for students to prepare for the examination.

Reviewer: Elias Shiu (Iowa City)

### MSC:

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

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

91B30 | Risk theory, insurance (MSC2010) |