If we look at a particular individual,
we see that there can be an extremely large variation inposible outcomes, each with a specific economic consequence.
By purchasing an insurancepolicy, 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 thetotal risk of the n individuals.
In reality, the risk assumed by the insurer is smaller in total than thesum of the risks associated with each individual policyholder.
These results are shown in the following theorem.