If we look at a particular individual, we see that there can be an extremely large variation in
possible outcomes, each with a specific economic consequence. By purchasing an insurance
policy, the individual transfers this risk to an insurance company in exchange for a fixed premium.
We might conclude, therefore, that if an insurer sells n policies to n individuals, it assumes the
total risk of the n individuals. In reality, the risk assumed by the insurer is smaller in total than the
sum of the risks associated with each individual policyholder. These results are shown in the
following theorem.