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

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322 Actuarial Modelling of Claim Counts Table 8.21 Evolution of the transient relativities for the steady-state initial distribution for the former Belgian compulsory bonus-malus scale with a super bonus level 0. Level l r 0 l r 10 l r 20 l r 30 l r 40 l r 50 l 22 000 % 25793 % 26951 % 27415 % 27744 % 28011 % 21 000 % 22081 % 23992 % 24691 % 25134 % 25473 % 20 000 % 19252 % 21680 % 22592 % 23139 % 23543 % 19 000 % 17466 % 19788 % 20813 % 21460 % 21940 % 18 000 % 16052 % 18299 % 19397 % 20107 % 20636 % 17 000 % 12472 % 16258 % 17829 % 18756 % 19409 % 16 000 % 11795 % 15198 % 16793 % 17767 % 18458 % 15 000 % 11134 % 14253 % 15879 % 16904 % 17634 % 14 000 % 11543 % 13902 % 15224 % 16158 % 16876 % 13 000 % 11181 % 13287 % 14580 % 15521 % 16252 % 12 000 % 6621 % 11164 % 13200 % 14479 % 15400 % 11 000 % 6849 % 10789 % 12722 % 13989 % 14915 % 10 000 % 6899 % 10357 % 12236 % 13514 % 14458 % 9 000 % 8004 % 10588 % 12130 % 13235 % 14095 % 8 000 % 7991 % 10209 % 11734 % 12854 % 13729 % 7 000 % 7824 % 7619 % 10195 % 11793 % 12933 % 6 000 % 7525 % 7520 % 9948 % 11511 % 12643 % 5 000 % 7118 % 7330 % 9651 % 11202 % 12341 % 4 000 % 7833 % 7660 % 9728 % 11137 % 12184 % 3 000 % 7315 % 7369 % 9424 % 10854 % 11921 % 2 000 % 6774 % 4242 % 7629 % 9672 % 11074 % 1 000 % 6228 % 4283 % 7507 % 9493 % 10874 % 0 000 % 9241 % 8794 % 8493 % 8485 % 8514 % Table 8.22 Relativies computed on the basis of the transient maximum accuracy criterion for the former Belgian compulsory bonus-malus scale with a super bonus level 0. Level l Uniform Top Steady state distribution ¯r l distribution ¯r l distribution ¯r l 22 2675 % 2410 % 2652% 21 2346 % 1848 % 2278% 20 2079 % 1633 % 1990% 19 1859 % 1468 % 1768% 18 1680 % 1338 % 1595% 17 1635 % 1234 % 1461% 16 1418 % 1149 % 1356% 15 1323 % 1078 % 1272% 14 1244 % 1018 % 1204% 13 1177% 966 % 1146% 12 1119% 921 % 1097% 11 1069% 880 % 1055% 10 1024% 844 % 1017%
Transient Maximum Accuracy Criterion 323 9 981% 810% 979% 8 940% 778% 944% 7 901% 748% 912% 6 865% 718% 881% 5 832% 691% 852% 4 783% 656% 798% 3 740% 624% 759% 2 703% 595% 723% 1 671% 566% 692% 0 655% 514% 876% 8.7 Further Reading and Bibliographic Notes There are relatively few papers dealing with the study of bonus-malus scales using transient distributions. The study of bonus-malus scales with transient distributions started with the seminal paper by Borgan, Hoem & Norberg (1981). Gilde & Sundt (1989) studied linear scales in a transient regime. The examples mentioned in this chapter (special scale for new entrants, and absorbing level 0) are extensively treated in Denuit, Maréchal, Pitrebois & Walhin (2007b).
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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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Credibility Models for Claim Counts
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