What does the law of large numbers state regarding insurance?

The law of large numbers is fundamental to the insurance industry, as it addresses the relationship between a large group of insured individuals and the predictability of losses. When applied to insurance, this law suggests that as the size of the group increases, the actual loss experience becomes more predictable and approaches the expected loss.

This occurs because, in a large group, individual variations in losses tend to average out. For instance, if a small number of people are insured, the loss experience may be influenced heavily by one or two members who have significant claims. However, when you expand the group size, the frequency and severity of those claims level off across the broader population, mirroring the insurance company's predictions based on statistical data.

In practical terms, this means that insurers can set their premiums more accurately and manage risk effectively due to the predictable nature of losses in large groups. This predictability allows for better underwriting and financial stability for the insurer, ultimately benefiting all policyholders through more stable rates and increased availability of coverage.