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ACTUARIAL MATHEMATICS

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Actuarial science is not static. In the time since the publication of the first edition of Actuarial Mathematics, actuarial science has absorbed additional ideas from economics and the mathematical sciences. At the same time, computing and communications have become cheaper and faster, and this has helped to make feasible more complex actuarial models. During this period the financial risks that modern societies seek to manage have also altered as a result of the globalization of business, technological advances, and political shifts that have changed public policies

It would be impossible to capture the full effect of all these changes in the re vision of a basic textbook. Our objective is more modest, but we hope that it is realistic. This edition is a step in an ongoing process of adaptation designed to keep the fundamentals of actuarial science current with changing realities.

In the second edition, changes in notation and nomenclature appear in almost every section. There are also basic changes from the first edition that should be

listed

1. Commutation functions, a classic tool in actuarial calculations, are not used. This is in response to the declining advantages of these functions in an age when interest rates are often viewed as random variables, or as varying deter- ministically, and the probability distribution of time until decrement may de- pend on variables other than attained age. Starting in Chapter 3, exercises that illustrate actuarial calculations using recursion formulas that can be imple mented with current software are introduced. It is logically necessary that the challenge of implementing tomorrow's software is left to the reader.

2. Utility theory is no longer confined to the first chapter. Examples are given that illustrate how utility theory can be employed to construct consistent models for premiums and reserves that differ from the conventional model that im- plicitly depends on linear utility of wealth..

3. In the first edition readers were seldom asked to consider more than the first and second moments of loss random variables. In this edition, following the intellectual path used earlier in physics and statistics, the distribution functions and probability density functions of loss variables are illustrated.

4. The basic material on reserves is now presented in two chapters. This facilitates a more complete development of the theory of reserves for general life insur- ances with varying premiums and benefits.

5. In recent years considerable actuarial research has been done on joint distri butions for several future lifetime random variables where mutual indepen dence is not assumed. This work influences the chapters on multiple life ac- tuarial functions and multiple decrement theory.

6. There are potentially serious estimation and interpretation problems in multiple decrement theory when the random times until decrement for competing causes of decrement are not independent. Those problems are illustrated in the second edition.
7. The applications of multiple decrement theory have been consolidated. No at tempt is made to illustrate in this basic textbook the variations in benefit for. mulas driven by rapid changes in pension practice and regulation.

8. The confluence of new research and computing capabilities has increased the use of recursive formulas in calculating the distribution of total losses derived from risk theory models. This development has influenced Chapter 12.

9. The material on pricing life insurance with death and withdrawal benefits and accounting for life insurance operations has been reorganized. Business and regulatory considerations have been concentrated in one chapter, and the foun dations of accounting and provisions for expenses in an earlier chapter. The discussion of regulation has been limited to general issues and options for addressing these issues. No attempt has been made to present a definitive interpretation of regulation for any nation, province, or state.

10. Thpreodels for some insurance products that are no longer important in the market have been deleted. Models for new products, such as accelerated ben- efits for terminal illness or long-term care, are introduced.

11. The final chapter contains a brief introduction to simple models in which in- terest rates are random variables. In addition, ideas for managing interest rate risk are discussed. It is hoped that this chapter will provide a bridge to recent developments within the intersection of actuarial mathematics and financial economics

As the project of writing this second edition ends, it is clear that a significant new development is under way. This new endeavor is centered on the creation of general models for managing the risks to individuals and organizations created by uncertain future cash flows when the uncertainty derives from any source. This blending of the actuarial/statistical approach to building models for financial se- curity systems with the approach taken in financial economics is a worthy assign- ment for the next cohort of actuarial students.

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Availability

10001248

368.01 BOW a 2nd

RLC MM (Rak Buku Umum)

Available

Detail Information

Series Title

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Statement of Responsibility

Newton L. Bowers

Call Number

368.01 BOW a 2nd

Publisher

Illinois : The Society of Actuaries., 1997

Collation

xxvi, 753 p. : ill ; 28cm.

Language

English

ISBN/ISSN

0-938959-46-8

Classification

368.01

Content Type

-

Edition

2nd. ed.

Subject(s)

Buku Umum
Actuarial Science
Actuarial Mathematics

Specific Detail Info

-

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