Law of large numbers in insurance

Jacob Bernoulli, Ars Conjectandi, published in 1713: the first proof of the law of large numbers. The observed average of many realizations of the same random event converges toward its expectation as the sample grows, and insurance takes its mathematical foundation from it. An insurer that pools many independent, similar risks sees the average claims cost per policy become more and more predictable, even though the individual claim remains uncertain. That is what allows a stable premium to be priced and risk to be pooled. The condition people tend to leave unspoken is independence. Strongly correlated risks materialize together, and pooling fails. A systemic cyberattack or the outage of a shared cloud provider hits many insureds at once, and a portfolio that looked diversified turns out to be concentrated. The AlgoPolis paper shows that the fully algorithmic firm, built on a single model, destroys cognitive diversification and so undermines the law of large numbers.