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By by Bjørn Sundt.

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An interesting question is of course, how much do we lose by applying the credibility scale instead of the Bayes scale for given bonus rules? To answer this question we introduce the credibility efficiency 7G. Let us now return to the general assumptions. We want to minimise with respect to a and b. 1 i) shows that the optimal choice of a and b is Thus for given R the optimal bonus scale is with under the bonus rules R. Numerical examples in Gilde & Sundt (1989) give relatively high values of the credibility efficiency, indicating that we do not lose much by applying the credibility scale instead of the Bayes scale.

Policy i is characterised by an unknown random risk parameter 6 i and has been observed for ni years. We assume that the 6 /S are conditionally independent and identically distributed given H. Let \j denote the claim amount of policy i in year j. We assume that Xil'Xi , ... are conditionally independent and identically distri2 -56- -57- buted with common distribution F( ·I O,TJ) given the values ()and 1J of 0 i and H. Let m{0i,H) = E[Xijl 0i,H); rp = EVar[Xi)0i,H); based on X. 32). t(H). t represents the over-all risk level for the whole portfolio, rp the fluctuations between claim amounts from an individual policy, and A the differences between policies within the same community.

1'" .. ,X. p. z ZJ The method of marginal totals can also be applied to other rating structures than multiplicative ones, in particular for additive rating models. In the last expression, yi is a qxl design vector based on observable technical data of the car model; in Uni Storebrand they apply (1, engine power, price/weight)' for The method of marginal totals and some other methods for determination of the parameters in multiplicative and additive rating models have been discussed by vehicle damage and (1, engine power, weight)' for third party liability.

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