Law of large numbers
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Definition
The convergence of observed loss experience to expected loss experience as the number of independent exposures rises.
Law of large numbers in plain English
An insurer cannot price one house fire with confidence, but ten thousand similar homes start to behave. Law of large numbers is the convergence of observed loss experience toward expected loss experience as the number of independent exposures rises. That is why pooling works and why a single anecdote is a terrible pricing model. It is an insurance foundation idea, not a stock-market diversification slogan. Bigger independent pools producing more predictable losses is law of large numbers at work.
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