Which mathematical concept is related to the certainty of predicting future losses?

The law of large numbers is fundamental to insurance as it describes how, as the number of trials or observations increases, the average of the results will get closer to the expected value. In the context of predicting future losses, this principle demonstrates that the more data an insurer accumulates on past claims, the more accurately they can predict future losses. This helps insurers to set premiums and manage their risk more effectively.

The law of large numbers assures insurers that with a large enough pool of policies, the statistical predictions about losses become more reliable. Consequently, it allows for a more accurate calculation of loss ratios and other financial metrics. This reliability in predictions aids insurers in their financial planning and risk management strategies, ultimately enhancing their capacity to serve policyholders effectively over time.

In contrast, while the principle of probability pertains to the likelihood of an event occurring, and the central limit theorem relates to the distribution of sample means, they do not provide the same assurance of prediction over large datasets as the law of large numbers does. Risk assessment theory, while crucial in the overall assessment of risk, also does not specifically correlate to the predictability of future losses in the same definitive way that the law of large numbers does.