Riebesell method

When an insured wants to raise its limit, from 1 to 2 million then to 4 million, the insurer must say what each extra layer costs. Since claims are much more frequent in small amounts than in large ones, the price does not rise in proportion to the limit. The method proposed in 1936 by the German actuary Paul Riebesell for fire insurance offers a simple rule: each doubling of the limit multiplies the premium by a constant factor, for example 1.2, a 20 percent increase. Going from 1 to 2 million therefore costs 20 percent more, from 2 to 4 million another 20 percent, and so on. This rule implicitly corresponds to a Pareto-type severity distribution, which explains its plausibility for liability lines where large losses are rare but possible. It has remained popular in Europe, notably in liability reinsurance, for its simplicity and apparent consistency. Its limits are well known: applied to very high limits, it can produce inconsistent prices, and it ignores the actual shape of a given portfolio's loss distribution. Actuaries today prefer data-driven increased limit factors, but knowing it helps read a large share of the prices in use.