What is the primary benefit of having a law of large numbers in insurance?

The primary benefit of the law of large numbers in insurance is the accurate estimation of premiums and losses. This statistical principle states that as the size of a sample increases, the average of the sample will get closer to the expected value. In the context of insurance, when a company insures a large number of similar risks, it can predict with greater accuracy the total number of claims that will arise and the total losses that will be incurred.

This forecasting ability enables insurers to set premiums that appropriately reflect the expected risks and potential payouts. A large pool of insured individuals results in a more reliable statistical analysis, which helps in establishing a well-balanced premium that covers anticipated claims while generating sufficient revenue for the company. This accuracy in the estimation process is crucial for the financial health and sustainability of insurance companies.

In addition, while other aspects such as lowering premiums, paying all claims, and guaranteeing profit margins may have their merits, they are not direct benefits of the law of large numbers. Rather, those aspects are influenced by a well-functioning actuarial process, which is enhanced by understanding large sample behaviors, as outlined by the law of large numbers.