This book introduces a statistical method, regression analysis. The introduction is organized around the traditional triad of statistical inference:
- hypothesis testing,
- estimation and
- prediction.
Further, this book shows how this methodology can be used in applications that are likely to be of interest to actuaries and to other risk analysts. As such, it is helpful to begin with the three traditional areas of actuarial applications:
- pricing,
- reserving and
- solvency testing.
Pricing and adverse selection. Regression analysis can be used to determine insurance prices for many lines of business. For example, in private passenger automobile insurance, expected claims vary by the insured’s gender, age, location (city versus rural), vehicle purpose (work or pleasure) and a host of other explanatory variables. Regression can be used to identify the variables that are important determinants of expected claims.
In competitive markets, insurance companies do not use the same price for all insureds. If they did, “good risks,” those with lower than average expected claims, would overpay and leave the company. In contrast, “bad risks,” those with higher than average expected claims, would remain with the company. If the company continued this flat rate pricing policy, premiums would rise (to compensate for claims by the increasing share of bad risks) and market share would dwindle as the company loses good risks. This problem is known as “adverse selection.” Using an appropriate set of explanatory variables, classification systems can be developed so that each insured pays their fair share.
Reserving and solvency testing. Both reserving and solvency testing are concerned with predicting whether liabilities associated with a group of policies will exceed the capital devoted to meeting obligations arising from the policies. Reserving involves determining the appropriate amount of capital to meet these obligations. Solvency testing is about assessing the adequacy of capital to fund the obligations for a block of business. In some practice areas, regression can be used to forecast future obligations to help determine reserves (see, for example, Chapter 19). Regression can also be used to compare characteristics of healthy and financially distressed firms for solvency testing (see, for example, Chapter 14).
Other risk management applications. Regression analysis is a quantitative tool that can be applied in a broad variety of business problems, not just the traditional areas of pricing, reserving and solvency testing. By becoming familiar with regression analysis, actuaries will have another quantitative skill that can be brought to bear on general problems involving the financial security of people, companies and governmental organizations. To help you develop insights, this book provides many examples of potential “non-actuarial” applications through featured vignettes labeled as “examples” and illustrative data sets.
To help understand potential regression applications, start by reviewing the several data sets featured in the Chapter 1 Exercises. Even if you do not complete the exercises to strengthen your data summary skills (that require the use of a computer), a review of the problem descriptions will help you become more familiar with types of applications in which an actuary might use regression techniques.