What does the Law of Large Numbers enable insurance actuaries to do?

The Law of Large Numbers is a fundamental principle in insurance and probability that describes how the larger the number of similar risks evaluated, the more accurately the expected outcomes can be predicted. This principle allows insurance actuaries to calculate losses among a large number of similar risks with increased precision.

When actuaries accumulate data from a broad base of policyholders, they recognize patterns and trends that emerge over time. By analyzing extensive data sets, they are able to estimate average losses and thereby set premiums in a way that helps ensure the financial stability of the insurance company. The larger the pool, the more reliable and predictable the statistical outcomes become, allowing for greater accuracy in risk assessment.

In contrast, trying to predict claims for a single policyholder or assessing risk in a small group lacks the statistical reliability that the Law of Large Numbers provides. Additionally, while the law improves estimates of average outcomes, it cannot determine the exact probability of loss for every individual, as individual circumstances and risks can vary widely. Thus, the correct answer—calculating losses among a large number of similar risks—is a direct application of this principle and reflects its significance in actuarial science.