| Classical Premium Calculation Principles |
| Written by theoretic |
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One of the basic questions of an insurance business is how one chooses a premium in order to cover the losses over time, described by the total claim amount process S. We think of the premium income p(t) in the portfolio of those policies where the claims occur as a deterministic function. A coarse, but useful approximation to the random quantity S(t) is given by its expectation ES(t). Based on the results of Sections 3.1.1 and 3.1.2 for the renewal model, we would expect that the insurance company loses on average if p(t) < ES(t) for large t and gains if p(t) > ES(t) for large t. Therefore it makes sense to choose a premium by “loading” the expected total claim amount by a certain positive number p. For example, we know from Proposition 3.1.3 that in the renewal model ES(t) = A EX\ £ (1 + o(1)), £ —> oo . Therefore it is reasonable to choose p(t) according to the equation p(t) = (1 + p) ES(t) or p(t) = (1 + p) XEXi t, (3.1.6) for some positive number p, called the safety loading. From the asymptotic results in Sections 3.1.1 and 3.1.2 it is evident that the insurance business is the more on the safe side the larger p. On the other hand, an overly large value p would make the insurance business less competitive: the number of contracts would decrease if the premium were too high compared to other premiums offered in the market. Since the success of the insurance business is based on the strong law of large numbers, one needs large numbers of policies in order to ensure the balance of premium income and total claim amount. Therefore, premium calculation principles more sophisticated than those suggested by (3.1.6) have also been considered in the literature. We briefly discuss some of them. |