Actuarial Modelling of Claim Counts Risk Classification, Credibility ...

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316 Actuarial Modelling of Claim Counts Cn 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 1 2 3 4 5 6 7 8 Age of policy Figure 8.3 Convergence of the transient policyholders’ distributions to the steady state distribution for the system −1/ + 2. The corresponding relativies ¯r l are presented in Table 8.15 for a uniform distribution of age of policy. The last column gives the steady state relativities. We notice that the relativities are more severe when the initial distribution is closer to the bottom initial distribution. This seems reasonable since, with the bottom initial distribution, many policyholders are in the bonus level from the beginning. Therefore, the bonus must be weaker and the maluses stronger to ensure the financial balance. As for the −1/top bonus-malus scale, the relativities obtained starting from the bottom initial distribution are the closest to the stationary relativities. Influence of the Maturity of the Portfolio Let us consider the following three distributions of age of policy: Age of Mature Young Old policy portfolio portfolio portfolio 1 125 % 25 % 5 % 2 125 % 20 % 5 % 3 125% 15% 10% 4 125% 10% 10% 5 125% 10% 10% 6 125% 10% 15% 7 125% 5% 20% 8 125% 5% 25%
Transient Maximum Accuracy Criterion 317 Table 8.14 Evolution of the transient relativities for the different initial distributions (−1/+2 scale). Level l r 0 l r 1 l Uniform initial distribution r 2 l r 5 l r 7 l r 8 l r l 5 00 % 1886 % 2048 % 2503 % 2631 % 2652 % 2714% 4 00% 994 % 1673 % 2031 % 2088 % 2142 % 2185% 3 00% 972% 935 % 1586 % 1821 % 1838 % 1925% 2 00% 972% 971 % 1323 % 1379 % 1378 % 1388% 1 00% 882% 863 % 1222 % 1210 % 1276 % 1286% 0 00% 882% 792% 674% 678% 680% 685% Level l r 0 l r 1 l r 2 l Top initial distribution r 5 l r 7 l r 8 l r l 5 00 % 1815 % 1820 % 2278 % 2546 % 2547 % 2714% 4 00% 883 % 1602 % 1987 % 1888 % 2126 % 2185% 3 00% 972% 794 % 1292 % 1772 % 1661 % 1925% 2 00% 972% 971 % 1313 % 1358 % 1358 % 1388% 1 00% 882% 863 % 1210 % 1082 % 1255 % 1286% 0 00% 882% 792% 616% 616% 660% 685% Level l r 0 l r 1 l Bottom initial distribution r 2 l r 5 l r 7 l r 8 l r l 5 00 % 2420 % 2817 % 2764 % 2735 % 2734 % 2714% 4 00 % 1850 % 2154 % 2178 % 2180 % 2183 % 2185% 3 00% 972 % 1554 % 1887 % 1910 % 1915 % 1925% 2 00 % 1627 % 1448 % 1408 % 1415 % 1394 % 1388% 1 00% 882 % 1447 % 1349 % 1281 % 1307 % 1286% 0 00% 882% 792% 724% 708% 699% 685% Table 8.15 Relativities computed on the basis of the transient maximum accuracy criterion (influence of the initial distribution). Level l Uniform Top Bottom Steady state distribution ¯r l distribution ¯r l distribution ¯r l distribution r l 5 2326 % 2071 % 2749 % 2714% 4 1643 % 1231 % 2140 % 2185% 3 1318 % 1074 % 1847 % 1925% 2 1145% 952 % 1447 % 1388% 1 994% 839 % 1317 % 1286% 0 710% 634% 759% 685%
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Contents Foreword Preface Notation
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Contents vii 2.4 Overdispersion 79
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Contents ix 4.2.3 Trajectory 170 4.
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Contents xi 7.4 Numerical Illustrat
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Part I Modelling Claim Counts Actua
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3 Credibility Models for Claim Coun
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Credibility Models for Claim Counts
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Page 323 and 324: 8 Transient Maximum Accuracy Criter
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Page 375 and 376: Bibliography Albrecht, P. (1983a).
Page 377 and 378: Bibliography 347 Daengdej, J., Luko
Page 379 and 380: Bibliography 349 Greenwood, M., & Y
Page 381 and 382: Bibliography 351 Norberg, R. (1976)
Page 383: Bibliography 353 Walhin, J.-F., & P
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