Under which method do actuaries determine rates based on the "law of large numbers"?

The method where actuaries determine rates based on the "law of large numbers" is manual rating. This approach relies on statistical data to anticipate future claims and establish rates accordingly. The law of large numbers suggests that as the number of exposures increases, the actual loss experience will converge on the expected loss experience. This is fundamental in insurance as it allows insurers to predict losses more accurately over a larger pool of policies.

In manual rating, insurers compile comprehensive data about past losses and use this information to create standardized rates for different types of risks. This effectively balances the risk as statistically, with a larger dataset, the variances in losses are more predictable, contributing to the overall stability and reliability of the rates charged to policyholders.

Other methods, like judgment rating, rely on the subjective experience and opinion of the underwriter rather than large-scale statistical analysis. Loss cost rating involves using loss data but focuses on the pure cost of losses without considering expenses or profit margins in the same structured way that manual rating does. Merit rating adjusts rates based on an individual policyholder's loss experience, rather than relying on the broader statistical analysis across many policyholders.