In collective behaviors regarding insurance, what does the law of large numbers ensure for the insurance company?

The law of large numbers is a fundamental concept in insurance that states as the number of exposure units increases, the actual results will more closely approximate the expected results. In the context of insurance, this principle ensures that an insurance company can make accurate mortality predictions by observing a large enough number of individuals.

As a risk pool expands, the variations in actual outcomes (like the number of insured individuals who pass away in a given period) become more predictable and align more closely with the statistical averages. This predictability aids in underwriting, pricing, and reserving, allowing insurance companies to set premiums that reflect the true level of risk associated with insuring a large group of people. Therefore, accurate mortality predictions enable insurers to manage their risk effectively, ensuring financial stability and the capacity to pay claims as they arise.