Economics of insurance coverage

The risk-shifting and distribution requirements highlighted in Le Gierse (and addressed below) reflect the economics of insurance coverage. Insurance premiums for one year of coverage, for example, exceed the expected cost of coverage (which equals the cost of a claim times the probability that a valid claim will be made) because the premiums have to cover the cost of claims paid and other costs, including administrative costs incurred by the insurer. Insureds are willing to pay this amount to transfer the risk of incurring a sizable financial
loss that would arise if the covered contingency in fact occurs.

The insurer benefits by pooling a given risk with numerous other assumed risks. The expected value of the losses incurred by the insurer, per dollar of premium income, remains unchanged as a life insurer provides life insurance coverage to an increasing number of (equally situated) insureds.

The actual losses assumed by the insurer may differ from expected losses so that an insurer’s total losses may exceed its expectations.10 The spread of the risk of loss (or possibility that the insurer will incur a very large loss) per premium dollar decreases, however, as more insureds are covered, as a result of the statistical
law of large numbers. Consequently, the loss incurred per premium dollar gets increasingly more predictable as the insurer covers a larger number of insureds. The Seventh Circuit described the law of large numbers as follows,

One thousand persons at age 30 pay $450 each for a one year policy with a death benefit of $200,000. In a normal year two of these persons will die, so the insurer expects to receive $450,000 and disperse $400,000. Of course, more may die in a given year than the actuarial tables predict. 

But as the size of the pool increases the law of large numbers takes over, and the ratio of actual to expected loss converges on one. The absolute size of the expected variance [spread] increases, but the ratio decreases. 

Insurers determine the expected value of losses per premium dollar (400/450 in the Seventh Circuit’s example) and the spread (riskiness) of actual/expected losses incurred using actuarial principles. Insurance coverage involving more than one period also involves risk-shifting and distribution although the analysis is more complex than that examined above.