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Regression Modeling with Actuarial and Financial Applications

Edward W. Frees
Cambridge University Press
Publication Date: 
Number of Pages: 
International Series on Actuarial Science
[Reviewed by
Ita Cirovic Donev
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Regression modeling is (by far) one of the most used statistical methods in the fields of finance and insurance, even though the method is, in most cases, taken for granted. What I mean by taken for granted is that most practitioners (who do not have a background in mathematics) consider the methods as a side note to their general daily tasks, not considering that, in most cases, these methods actually provide the means for them to make “proper” decisions or provide guidance. Considering this, a book that would provide the applied side and know-how while also emphasizing the importance of statistical theory is of great importance in these fields.

The book is divided into four parts: Linear Regression, Topics in Time Series, Topics in Nonlinear Regression, and Actuarial Applications. First part covers, as its title suggests, the main methods of linear regression including single and multivariable regression, selection of variables, and how to interpret regression results. This alone fills around 200 pages of the book, so it is not just an introduction. The regression methods are covered in detail with plenty of illustrative examples and computer output. The author provides quite a lot of guidance as to why and when certain methods are applied and most importantly how.

In part II, Topics in Time Series, we change the scenery a bit. Now the reader must change the concepts of data structure in his mind and consider a dataset given with a time scale. The study of time series is an important area of statistics that is often forgotten in practice, since many “good looking” graphs can be drawn and often conclusions reached without much application of actual time series methods. The author starts the section with an example to illustrate different types of methods. This section differs slightly from most books on time series in its notation and form of presentation, but it nevertheless does cover the basic concepts. Here the details are omitted and one should consult additional books to gain deeper understanding of the subject.

Part III, Topics in Nonlinear Regression, covers categorical dependent variables, count dependent variables, GLM, survival models, and other miscellaneous topics. These are all very important topics for measuring credit risk in financial institutions. The main concepts are presented, but the emphasis is on the general understanding of the concepts, without much detail as to the theoretical methods or bigger examples.

Overall, I would recommend the book to practitioners with intermediate background in statistics, in order to get the “feeling“ for the concepts and prepare them to consult a more advanced text to learn the finesse of the subject, which is also very much needed in industry applications.

Ita Cirovic Donev holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical methods for credit and market risk. Apart from the academic work she does statistical consulting work for financial institutions in the area of risk management.

1. Regression and the normal distribution; Part I. Linear Regression: 2. Basic linear regression; 3. Multiple linear regression – I; 4. Multiple linear regression – II; 5. Variable selection; 6. Interpreting regression results; Part II. Topics in Time Series: 7. Modeling trends; 8. Autocorrelations and autoregressive models; 9. Forecasting and time series models; 10. Longitudinal and panel data models; Part III. Topics in Nonlinear Regression: 11. Categorical dependent variables; 12. Count dependent variables; 13. Generalized linear models; 14. Survival models; 15. Miscellaneous regression topics; Part IV. Actuarial Applications: 16. Frequency-severity models; 17. Fat-tailed regression models; 18. Credibility and bonus-malus; 19. Claims triangles; 20. Report writing: communicating data analysis results; 21. Designing effective graphs; Appendix 1: basic statistical inference; Appendix 2: matrix algebra; Appendix 3: probability tables.