It should be clear that the existence of a private insurance industry in and of itself does not decrease the frequency or severity of loss. Viewed another way, merely entering into an insurance contract does not change the policyholder’s expectation of loss. Thus, given perfect information, the amount that any policyholder should have to pay an insurer equals the expected claim payments plus an amount to cover the insurer’s expenses for selling and servicing the policy, including some profit. The expected amount of claim payments is called the net premium or benefit premium. The term gross premium refers to the total of the net premium and the amount to cover the insurer’s expenses and a margin for unanticipated claim payments.
Insurance example
Going back to our example of the car owner, consider an insurance company that will
reimburse repair costs resulting from accidents for 100 car owners, each with the same risks as in
our earlier example. Each car owner has an expected loss of 750 and a standard deviation of
2442. As a group the expected loss is 75,000 and the variance is 596,250,000. The standard
deviation is 596,250,000 = 24,418which is significantly less than the sum of the standard
deviations, 244,182. The ratio of the standard deviation to the expected loss is
24,418 75,000 = 0.326 , which is significantly less than the ratio of 2442 750 = 3.26 for one car
owner.
It should be clear that the existence of a private insurance industry in and of itself does not decrease the frequency or severity of loss. Viewed another way, merely entering into an insurance contract does not change the policyholder’s expectation of loss. Thus, given perfect information, the amount that any policyholder should have to pay an insurer equals the expected claim payments plus an amount to cover the insurer’s expenses for selling and servicing the policy, including some profit. The expected amount of claim payments is called the net premium or benefit premium. The term gross premium refers to the total of the net premium and the amount to cover the insurer’s expenses and a margin for unanticipated claim payments.
It should be clear that the existence of a private insurance industry in and of itself does not decrease the frequency or severity of loss. Viewed another way, merely entering into an insurance contract does not change the policyholder’s expectation of loss. Thus, given perfect information, the amount that any policyholder should have to pay an insurer equals the expected claim payments plus an amount to cover the insurer’s expenses for selling and servicing the policy, including some profit. The expected amount of claim payments is called the net premium or benefit premium. The term gross premium refers to the total of the net premium and the amount to cover the insurer’s expenses and a margin for unanticipated claim payments.
