What does the Law of Large Numbers suggest in insurance?

The Law of Large Numbers in insurance indicates that as the number of units or observations increases, the average outcome becomes more predictable. This principle is a foundational concept in insurance because it allows insurers to estimate future losses with greater accuracy based on historical data.

When an insurance company has a vast number of insured units (such as cars, homes, or policies), it can gather enough data to identify trends and patterns in claims. This leads to a more reliable actuarial prediction of how much they will need to pay out in claims over time. For instance, if an insurance company insures 10,000 cars, it can reasonably predict the average number of accidents and their costs based on past data. However, if they only insured a few cars, the variability and unpredictability of claims would be much higher due to insufficient data.

This concept is critical in setting premiums and reserves effectively, ensuring that the insurer has sufficient funds to cover potential claims. As the number of policies increases, the impact of random variations diminishes, allowing for a more stable and predictable estimation of losses. This predictive ability is vital for the financial health of insurance companies and the broader insurance market.