The principle that the average loss of a large portfolio of independent risks becomes predictable.
The law of large numbers is the mathematical foundation of insurance. It states that the observed average of a large number of realizations of the same random event converges toward its theoretical expectation as the sample size grows. Applied to insurance, it means that if an insurer pools a large number of independent, similar risks, the average claims cost per policy becomes increasingly predictable, even though the individual claim remains uncertain. This is what allows a stable premium to be priced and risk to be mutualized among policyholders. The essential condition, often left unspoken, is the independence of risks. The law of large numbers works only if claims are uncorrelated, because strongly correlated risks can materialize simultaneously and defeat risk pooling. This is precisely what threatens the insurability of certain modern perils. A systemic cyberattack or the failure of a shared cloud provider strikes many insureds at once, violating the independence assumption and turning an apparently diversified portfolio into a concentrated exposure. The AlgoPolis paper shows that the fully algorithmic firm, built on a single model, destroys cognitive diversification and thereby makes the law of large numbers waver.
A motor insurer can accurately forecast the average cost of accidents across a million independent drivers, but that predictability collapses if all its insureds rely on a single faulty driving software.
loi des grands nombres, law of large numbers, mutualisation