What does the law of large numbers imply in the context of insurance?

The law of large numbers is a fundamental principle in the field of probability and statistics that is particularly relevant in the context of insurance. It states that as the number of trials or events increases, the average of the outcomes will converge to the expected value. In insurance, this translates to the idea that with a large enough number of insured events (e.g., claims), the actual loss incurred by the insurer will tend to align closely with the anticipated or expected losses calculated based on probability and historical data.

This principle is crucial for insurers when setting premiums and managing risk, as they rely on statistical models to predict losses over a large population of policyholders. The convergence of actual losses to expected losses helps ensure that the insurer remains financially viable, as it can predict its liabilities more accurately over time.

While it may be possible for actual losses to vary significantly in the short term or for small sample sizes, the law of large numbers assures that these variations will diminish as the number of events increases, thus leading to the conclusion that the actual loss per event will equal the expected loss per event in a sufficiently large dataset. This understanding aids insurers in their underwriting practices and financial planning.