Probability, Statistics, and Mathematics

Abstract

P.A. Samuelson (1963) pointed out a widespread fallacy concerning how insurance works: It is not by adding independent risks that risk exposure is eased but by subdividing through pooling the added risks. Insuring 100 independent ships increases risk 10-fold over insuring one ship; by pooling risk coverage of the 100 over 100 insurers, one reduces the risk on each to effectively one-tenth. Riskiness does not cancel out for the long-term investor in a random-walk course but rather grows like . These law-of-large-number and central-limit-law truths do not justify the belief that when a favorable bet is repeatable a large enough number of times, it must end one up ahead.