How does the law of large numbers apply to insurance risk assessment?

The law of large numbers plays a crucial role in insurance risk assessment by stating that as the number of exposure units increases, the actual loss experience will more closely approximate the expected loss. This concept hinges on the idea that while individual outcomes may vary widely, the average outcomes will stabilize when aggregated over a larger group.

By writing more policies, insurers create a more extensive data set that allows for more accurate predictions of overall losses and claims. This is because, with a larger pool of insureds, the variability of losses tends to diminish, thereby enabling the insurer to predict future claims with better precision. This relationship enhances the insurer's ability to set premiums appropriately and ensures solvency through a balanced risk pool.

In contrast, the other options do not align with the way the law of large numbers operates. For instance, predicting exact loss amounts for individual policies does not follow this principle, as individual claims can vary significantly. Also, fewer policies do not validate predictions as effectively since smaller samples tend to produce greater variability and uncertainty in outcomes. Finally, the law does not operate independently of claim frequency; rather, it directly relates to the aggregation of many similar risks to achieve a more stable estimate of losses.