Risk theory. The stochastic basis of insurance. 3rd ed.

*(English)*Zbl 0532.62081
Monographs on Statistics and Applied Probability. London - New York: Chapman and Hall. XVII, 408 p. £11.95 (1984).

Since the publication of the first edition of this book in 1969 (see Zbl 0195.483), risk theory has developed quickly, especially so in the last decade, what is reflected by the fact that there is a much greater difference between the now available third edition and the second of 1977 (see Zbl 0405.62079), than between the first two editions.

The book is written in the same spirit, though, as its two predecessors. Emphasis is not in the first place on abstraction and completeness of mathematical theory but rather on practical applications of mathematical stochastics in the (mostly non-life) insurance business. Recent developments of insurance mathematics in theories and applications together with the propagation of high speed and increasingly comfortable computers are taken into account by some new or enlarged topis such as solvency, reserve techniques, and ruin theory as well as by changes of representation.

To sum up, the book is a useful and up-to-date introduction into applied risk theory, and of interest to anyone working within the actuarial field.

The book is written in the same spirit, though, as its two predecessors. Emphasis is not in the first place on abstraction and completeness of mathematical theory but rather on practical applications of mathematical stochastics in the (mostly non-life) insurance business. Recent developments of insurance mathematics in theories and applications together with the propagation of high speed and increasingly comfortable computers are taken into account by some new or enlarged topis such as solvency, reserve techniques, and ruin theory as well as by changes of representation.

To sum up, the book is a useful and up-to-date introduction into applied risk theory, and of interest to anyone working within the actuarial field.

Reviewer: W.-R.Heilmann

##### MSC:

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

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

60K10 | Applications of renewal theory (reliability, demand theory, etc.) |

90B99 | Operations research and management science |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |