How does the Law of Large Numbers impact insurance pools?

The Law of Large Numbers is a fundamental statistical principle that states that as the number of observations (or trials) increases, the actual outcomes will tend to get closer to the expected value. In the context of insurance, this principle has significant implications for how insurance pools function.

When an insurance company pools together a larger number of policyholders, the variation in individual losses tends to average out. Thus, the total expected losses for the insurance pool become more predictable. This predictability is crucial for insurers because it allows them to set premiums that reflect the true risk associated with the policies they write.

As the size of the insurance pool increases, the insurer can more accurately estimate the likelihood and severity of claims based on historical data. This leads to better pricing strategies and helps in maintaining the financial stability of the insurance company. The advantages provided by the Law of Large Numbers enable insurers to operate effectively, ensuring they can meet their obligations to policyholders while also remaining profitable.

The other aspects related to the question, such as individual claims becoming larger or uncertainty increasing, do not align with the core function of the Law of Large Numbers, which fundamentally supports accuracy in predicting total losses. Similarly, the principle does not dictate that all policyholders pay the same premium, as