Law of Large Numbers
The statistical principle that the larger the number of similar exposure units observed, the more closely actual losses will match expected losses. It is the foundation of predictable insurance pricing.
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The law of large numbers makes insurance possible primarily because:
As the number of similar, independent exposures grows, actual losses move closer to expected losses — The law of large numbers holds that the greater the number of similar, independent exposures, the closer actual results come to expected results. Insurers use this statistical certainty to set premiums that will cover anticipated claims and expenses. The law predicts the aggregate, never the individual. Larger, more homogeneous pools produce more reliable pricing, which is why insurers seek broad participation in every line, including health and disability.
National insurance concept
For the law of large numbers to improve the accuracy of loss prediction, the exposures within the pool should be:
Similar, so they are subject to approximately the same chance of loss — The law of large numbers works best when exposures are similar and homogeneous — subject to roughly the same chance of loss. Homogeneity lets the actuary treat the group as one statistical population and estimate expected claims from its aggregate experience. This is why insurers classify risks into groups such as age, health, and occupation rather than mixing fundamentally different exposures into a single pool.
National insurance concept
- General InsuranceThe law of large numbers makes insurance possible primarily because:
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