South Dakota Crop Insurance Practice Exam

What statistical principle allows actuaries to estimate future losses in insurance?

1. The law of averages

2. The law of large numbers

3. Probability theory

4. The principle of indemnity

The correct answer is: The law of large numbers

The law of large numbers is the statistical principle that enables actuaries to estimate future losses in insurance with a high degree of accuracy. This principle states that as the size of a sample increases, the sample mean will get closer to the expected value (or population mean). In the context of insurance, as more policies are written and more claims are observed, the average losses can be predicted more reliably. Actuaries use this principle to analyze historical data on claims and losses from similar insurance policies. This statistical foundation allows them to make informed predictions about future losses based on observed trends, thus ensuring that the insurance pool is adequately funded to cover potential claims. The distinction between this and other principles is important. For example, probability theory underpins the mathematical foundations of these estimates but does not specifically address the behavior of averages in larger samples. The law of averages is a general observation related to predictions over time but does not have the rigorous statistical backing that the law of large numbers does. The principle of indemnity relates to compensation in insurance, ensuring that claims do not exceed the insured value, but it does not directly explain how future losses are estimated. This highlights the significance and applicability of the law of large numbers in the field of insurance actuarial science.