Reference no: EM132819541

Case Study of: The Law of Large Numbers

The Law of Large Number availability of only small data sources (or sometimes none at all) is troublesome because most estimation techniques rely on numerous observations for accuracy. The benefit of many observations is well stated by the law of large numbers, an important statistical doctrine for the successful management of risk and the basic foundation for the existence of insurance in society. The law of large numbers holds that, as a sample of observations increases in size, the relative variation about the mean declines. The important point is that, with larger samples, we feel more confident in our estimates. If it were not for the law of large numbers, insurance would not exist. A risk manager (or insurance executive) uses the law of large numbers to estimate future outcomes for planning purposes. The larger the sample size, the lower the relative risk, everything else being equal. The pooling of many exposures gives the insurer a better prediction of future losses. The insurer still has some risk or variability around the average. Nevertheless, the risk of an insurer with more exposures is relatively lower than that of an insurer with fewer exposures under the same expected distribution of losses. More Exposures, Less Risk". The importance of the large number of exposures often prompts the question. What can smaller insurers do to reduce the uncertainty in predicting losses? Smaller insurers use the sharing of data that exists in the insurance industry. One such data collection and statistical analysis organization is the Insurance Services Office (ISO). In addition to being a statistical agent, this organization provides the uniform policy forms for the property/casualty industry (a small sample of these policies are in the appendixes at the end of the text). The ISO is both a data collection agent and an advisory organization to the industry on matters of rates and policy forms.

From the above case study, analyze the advantages of the law of large number implemented in the insurance industry.