What principle does the law of large numbers rely on for insurance predictions?

The law of large numbers is a fundamental principle in statistics and insurance that asserts the accuracy of predictions improves as the size of the sample increases. In the context of insurance, this means that when a large number of policyholders are pooled together, the overall behavior of the group can be predicted more reliably compared to a small group.

This principle operates on the idea that while individual claims and events may fluctuate or vary widely, the average of the outcomes becomes more stable as more instances are included in the analysis. For insurance companies, this translates to being able to set premiums based on predicted losses with greater confidence when spreading risk over a larger pool of insured individuals. As the risk pool grows, the insurer can more effectively manage the risk of paying out claims, leading to more accurate predictions of payouts and financial outcomes.

In contrast to this, relying on individual case studies, using a small sample size, or managing solely high-risk profiles can lead to skewed data and unreliable predictions. Smaller samples may not accurately represent the larger population, increasing the variability and uncertainty in outcomes. Hence, the law of large numbers underscores the importance of having a broad risk pool to facilitate better prediction and management of insurance risks.