Abstract
The law of large numbers (or the related central limit theorem) is used in the literature on risk management and insurance to explain pooling of losses as an insurance mechanism. Also called the “law of averages”, the principle holds that the average of a large number of independent identically distributed random variables tends to fall close to the expected value. This result can be used to show that the entry of additional risks to an insured pool tends to reduce the variation of the average loss per policyholder around the expected value.1 When each policyholder’s contribution to the pool’s resources exceeds the expected loss payment, the entry of additional policyholders reduces the probability that the pool’s resources will be insufficient to pay all claims. Thus an increase in the number of policyholders strengthens the insurance by reducing the probability that the pool will fail.2
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Smith, M.L., Kane, S.A. (1994). The Law of Large Numbers and the Strength of Insurance. In: Gustavson, S.G., Harrington, S.E. (eds) Insurance, Risk Management, and Public Policy. Huebner International Series on Risk, Insurance and Economic Security, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1378-6_1
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DOI: https://doi.org/10.1007/978-94-011-1378-6_1
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