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Actuarial mathematics. (English) Zbl 0634.62107
Itasca, Illinois: The Society of Actuaries. XXIII, 624 p. (1986).
This is a comprehensive and up-to-date textbook on quantitative methods in insurance, written by five outstanding experts. Based on a stochastic approach it covers contingency theory as well as the related fields of risk theory, economics and population theory. The mathematics required does not involve ideas beyond those covered in an undergraduate program. The different chapters are:
1. The economics of insurance; 2. Individual risk models for a short term; 3. Survival distributions and life tables; 4. Life insurance; 5. Life annuities; 6. Net premiums; 7. Net premium reserves; 8. Multiple life functions; 9. Multiple decrement models;
10. Valuation theory for pension plans; 11. Collective risk models for a single period; 12. Collective risk models over an extended period; 13. Applications of risk theory; 14. Insurance models including expenses; 15. Nonforfeiture benefits and dividends; 16. Special annuities and insurances; 17. Advanced multiple life theory; 18. Population theory; 19. Theory of pension funding.
There is no risk in predicting that this excellent volume will be a standard textbook for many years.
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
91B30 Risk theory, insurance (MSC2010)
91-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance