What does the "law of large numbers" state in insurance?

The principle articulated by the "law of large numbers" in insurance is fundamentally about predictability across larger pools of similar risks. Specifically, it states that as the number of risks or exposures increases, the aggregate outcomes become more reliable and predictable. This allows insurers to estimate losses and set premiums with greater accuracy based on historical data.

When an insurer pools a larger number of similar risks, individual uncertainties tend to offset each other, leading to a more stable overall risk profile. For instance, when insuring a large group of drivers, the insurer can better predict the number of claims based on past experiences with similar groups. This predictability helps in creating appropriate pricing strategies that reflect the true risk while also ensuring that the insurer remains solvent and profitable.

Understanding this concept is crucial for the insurance industry as it underlies the effectiveness of using statistical methods for risk assessment and premium calculation. Ultimately, the law of large numbers supports the idea that insurance becomes more effective when risks are pooled together, allowing for a more stable and predictable outcome in financial planning and loss projections.