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

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Actuarial Modelling of Claim Counts Risk Classification, Credibility and Bonus-Malus Systems Michel Denuit Institut de Statistique, Université Catholique de Louvain, Belgium Xavier Maréchal Reacfin, Spin-off of the Université Catholique de Louvain, Belgium Sandra Pitrebois Secura, Belgium Jean-François Walhin Fortis, Belgium
Page 1: Actuarial Modelling of Claim Counts
Page 6 and 7: Copyright © 2007 John Wiley & Sons
Page 8 and 9: vi Actuarial Modelling of Claim Cou
Page 10 and 11: viii Actuarial Modelling of Claim C
Page 12 and 13: x Actuarial Modelling of Claim Coun
Page 15 and 16: Foreword Belgium has a long and dis
Page 17 and 18: Preface Motor Insurance This book i
Page 19 and 20: Preface xvii by competitors. This e
Page 21 and 22: Preface xix reality excellent drive
Page 23 and 24: Preface xxi French bonus-malus syst
Page 25 and 26: Preface xxiii This collaboration br
Page 27 and 28: Notation Here are a few words on th
Page 29: Notation xxvii • the Negative Bin
Page 33 and 34: 1 Mixed Poisson Models for Claim Nu
Page 35 and 36: Mixed Poisson Models for Claim Numb
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Mixed Poisson Models for Claim Numb
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2 Risk Classification 2.1 Introduct
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Risk Classification 51 sharing can
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Risk Classification 53 these claims
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Risk Classification 55 Number of po
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Risk Classification 59 13000 12000
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Risk Classification 63 Example 2.3
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Risk Classification 65 2.3.4 Multip
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Risk Classification 67 The computat
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Risk Classification 69 2.3.8 Wald C
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Risk Classification 71 2.3.11 Devia
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Risk Classification 73 with the Poi
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Risk Classification 75 used). The r
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Risk Classification 77 Table 2.2 Re
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Risk Classification 81 The unobserv
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Risk Classification 83 T 2 = ∑ n
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Risk Classification 85 and then wri
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Risk Classification 89 2.8 Risk Cla
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Table 2.7 A priori risk classificat
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Risk Classification 93 Frequency 0.
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Risk Classification 101 These resul
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Risk Classification 103 Modelling D
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Risk Classification 105 Table 2.12
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Risk Classification 107 PrN i1 = k
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Risk Classification 109 2.9.9 Vuong
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Risk Classification 111 Table 2.16
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Risk Classification 113 account for
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Risk Classification 115 Raw exposur
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Risk Classification 117 Geographic
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Part II Basics of Experience Rating
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122 Actuarial Modelling of Claim Co
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4 Bonus-Malus Scales 4.1 Introducti
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Bonus-Malus Scales 167 of this topi
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Bonus-Malus Scales 169 needed to go
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Bonus-Malus Scales 171 4.2.4 Transi
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Bonus-Malus Scales 173 4.3.2 Transi
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Bonus-Malus Scales 175 as p n l 1 l
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Bonus-Malus Scales 177 ⎛ P 3 01 =
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Bonus-Malus Scales 179 does not dep
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Bonus-Malus Scales 181 = 1 1 1 1 1
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Bonus-Malus Scales 183 (i) set A0 =
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Bonus-Malus Scales 185 4.5.2 Bayesi
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Bonus-Malus Scales 187 Table 4.3 Nu
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Bonus-Malus Scales 189 Table 4.7 Nu
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Bonus-Malus Scales 191 4.5.4 Linear
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Bonus-Malus Scales 193 Table 4.10 L
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Bonus-Malus Scales 195 Now, we have
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Bonus-Malus Scales 197 under the fi
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Bonus-Malus Scales 199 Table 4.14 N
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Bonus-Malus Scales 201 Table 4.17 T
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Bonus-Malus Scales 203 Table 4.19 N
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Bonus-Malus Scales 205 Table 4.21 R
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Bonus-Malus Scales 207 ∑16 j=13 r
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Bonus-Malus Scales 209 4.8.3 Distan
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Bonus-Malus Scales 211 Table 4.25 p
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Bonus-Malus Scales 213 We observe t
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Bonus-Malus Scales 215 No explicit
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5 Efficiency and Bonus Hunger 5.1 I
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Efficiency and Bonus Hunger 221 acc
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Efficiency and Bonus Hunger 223 The
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Efficiency and Bonus Hunger 225 For
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Efficiency and Bonus Hunger 227 tes
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Efficiency and Bonus Hunger 229 App
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Efficiency and Bonus Hunger 231 Let
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Efficiency and Bonus Hunger 233 Rem
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Efficiency and Bonus Hunger 235 Tab
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Efficiency and Bonus Hunger 237 We
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Efficiency and Bonus Hunger 241 Com
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Efficiency and Bonus Hunger 243 Loi
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Efficiency and Bonus Hunger 245 De
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Efficiency and Bonus Hunger 247 to
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Efficiency and Bonus Hunger 251 Mor
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Efficiency and Bonus Hunger 253 Fir
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Efficiency and Bonus Hunger 255 5.5
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Efficiency and Bonus Hunger 257 lik
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6 Multi-Event Systems 6.1 Introduct
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Multi-Event Systems 261 score bod i
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Multi-Event Systems 263 6.2.5 Varia
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Multi-Event Systems 265 of the true
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Multi-Event Systems 267 E [ N mat i
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Multi-Event Systems 269 Table 6.2 E
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Multi-Event Systems 271 Denoting as
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Multi-Event Systems 273 6.3.2 Marko
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Multi-Event Systems 275 P 2 = exp
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7 Bonus-Malus Systems with Varying
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Bonus-Malus Systems with Varying De
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9 Actuarial Analysis of the French
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Actuarial Analysis of the French Bo
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Index Binomial distribution 13-15,
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