(absolute loss function)186 - (posterior structure function)163 - (a priori rating variables)25 (Bayes scale) 178 (bancassurance)233 - (beta distribution)203, 204 (high deductible)218 (bonus)26 ( ) (total variation)133, 134, (sedentary, business drivers)35 - (effect of expense loadings) 207 - (observed distribution of number of claims)46 - (gamma distribution)203 - (gamma function) 51 (principal component)116 (global elasticity)102 - dynamic programming)103 (credibility scale)180 (bonus hunger, hunger for bonus)103 (index of toughness)122, 123 (contagion)54 (true ο) 54 (apparent ο) 54 (positive ο) 54 (overcharges) 196 (undercharges) 196 (simulation) 75, 91 (index of toughness) 122, 123 (true contagion) 54 (apparent contagion) 54 (quadratic loss function) 164 (conversion factor) 106 (skewness coefficient) 44 (ο of variation) 83 (credibility factor) 169 (loading ο) 208 (discount ο) 99, 105 (goodness-offit tests) 47 (Anderson Darling test) 49 (Kolmogorov Smirnov ο) 49 (Cramer von Mises ο) 49 - (generalized likelihood ratio ο) 70 (likelihood ratio ο) 69 χ 2 (χ-square-type ο) 49 χ 2 (χ 2 ο)49 (linear expense loadings) 209 - (logarithmic utility function) 238, 241
255 (log-normal distribution) 83, 106, 239 (malus) 26 - (Belgian BMS, Markovian presentation) 32 (median premium calculation principle) 186 À / Á (good-risk/bad-risk model) 57, 58 (multiline BMS) 184 (expense loadings) 207 (linear οο)21 2 - (allowance for severity of clams) 202 (level expense loadings) 212 (loading coefficient) 208 - (penalty (young drivers)) 81, 82 (implicit ο ο ο) 81,82 (heterogeneous portfolio) 50 - (nondeclaration of small claims) 103 (sedentary drivers) 35 - (implicit penalty (young drivers)) 81, 82 - (generalized inverse Gaussian distribution) 172 - (general mixed Poisson process) 175, - (ο ο ο ο, posterior structure function) 176, - (ο ο ο ο, posterior moments) 177 - (inverse Gaussian distribution) 55 (level expense loadings) 211 (homogeneous Markov chain) 33 (homogeneous portfolio) 42 - (optimal bonus-malus system) 165, (οοο, properties) 166 169 (ο deductible) 234, 240, 242 (optimal retention) 104, 110, 112 (RSAL) 77, 79 - (relative stationary average level) 77, 79 - (negative binomial model) 50 - (ο οοwith regression component) 180 (negative binomial distribution) 52, 53 - - (maximum likelihood estimates for negative binomial model) 53, 54 (οοοοpoisson model) 45, 46 / - (ο οοοο/inverse Gaussian model) 57 (exact οοο)57
256 - À / Á (moments method for good-risk/bad-risk model) 58 - (οοοοnegative binomial model) 53, 54 - (ο οοοpoisson model) 45, 46 / - (ο ο ο ο ο / inverse Gaussian model) 56 (transition matrix) 30 (transition rules) 29 - (Pearson skewness coefficient) 44 (total variation) 133, 134 (full stationarity) 79 (positive contagion) 54 (variance premium calculation principle) 188 - (median premium calculation ο) 187 (zero-utility ο) 192 - (expected value premium calculation ο) 166 (grouping procedure) 48 (business drivers) 35 (noncontagious process) 45 (straight deductible) 219 (Poisson model) 42 - (ο οwith regression component) 182 / - ( ) (Poisson/inverse Gaussian distribution (model)) 55, - (gamma loss severities) 224 (Pareto distribution) 239 III (Pearson type III ο) 51 - (observed ο of number of claims) 46, À - / Á, - (ο ο ο ο ο, goodrisk/bad-risk model, moments method) 58, -, - (ο ο ο ο ο, negative binomial model, maximum likelihood) 53,, - (ο ο ο ο ο, ο ο ο, moments method) 53, (οοοοο, Poisson model) 46, / -, - (οοοο ο, ο / inverse Gaussian model, maximum likelihood) 56, /, - (ο οοοο, ο / οο ο, moments method) 56 (regression component) 182 (regular Markov chain) 90 - (recursive calculation of stationary distribution) 93 (BMS) 26, 29
257, (high-deductible system) 218 - (bonus-malus ο) 26, 29 ( ) (οοοof Belgium (new)) 31, 32, 141 ( ) (ο οο ο (old)) 35, 140 (ο ο οοbrazil) 142 ( - ) (ο ο ο ο United Kingdom (protected)) 153 ( - ) (ο οοοοο (unprotected)) 152 ( ) (ο οο ο Germany (new)) 146 ( ) (οοο οο(old)) 145 (ο οοοhong Kong) 147 (οοοοdenmark) 142 (ο οοοspain) 143 ( ) (ο οοο Italy (new)) 148 ( ) (οοοο ο (old)) 147 (ο ο ο ο Kenya) 150 (ο ο ο ο Korea) 149, 150 ( ) (ο οοοluxembourg (new)) 151 ( ) (ο οοοο(old)) 151 (ο οο ο Malaysia) 148 (ο ο ο ο the Netherlands) 152 ( ) (ο οο ο Norway (new)) 155 ( ) (οοο οο(old)) 154 Portugal) 139 (ο ο ο ο (ο οοοsingapore) 148 88 (ο οοοthailand) 155 (ο ο ο ο Taiwan) 157 ( ) (ο ο οοfinland (new)) 144 ( )(οο οοο(old)) 143 (ο οοοfrance) 144 ( ) (ο ο οοswitzerland (new)) 156 ( )(οο οοο(old)) 156 (οοοοsweden) 153 ( )(οοοο Japan (new)) 149 ( )(οοοο ο (old)) 149 (convergence rate) 137 (compound Poisson) 83, 220 - (mixed Poisson distribution) 51 (mixing distribution) 51 - (eigenvalue of transition matrix) 91, 137 (eigenvector of transition matrix) 91 (perfect elasticity) 88 (conjugate distributions) 165 (average optimal retention) 112 (statistical game) 163 (stationary distribution) 90 95 (stationarity) 79
258 (fullο) 79 (collision insurance) 26,234 (structure function) 51 (posterior ο ο) 163 (Bayes theorem) 163,165,166,174 176 (exact maximum likelihood estimates) 57 (optimal retention) 110 (factor analysis) 116, (ο ο, factor scores) 120,123,c (ο ο,factor loading plot) 120, (ο ο,factor structure) 120, (οο, factor loadings) 120 (factors) 116 (credibility formula) 169,204 (Bessel function) 172 (utility ο) 192 (logarithmic οο) 238,241 (exponential οο) 192,198,238,240 (loss ο) 162 (absolute ο ο) 186 (quadratic οο) 164 (fourthdegree οο)187 (likelihood ο) 69 (risk ο) 162 (central valueof BMS) 96 (Markov chain) 30 (homogeneous ο ο) 30 (regular οο)90 (Bayes scale) 178 (credibility scale) 180 - (exponential utility function) 192, 198, 238, 240 (exponential distribution) 44, 239 (exponential losses) 219, 226 (elasticity) 87 (global ο) 102 (perfectο) 88, (asymptotic concept of ο) 88, 95, (transient concept of ο) 99 - (empirical optimal deductible) 234, 240, 242 (ergodic state) 90 (efficiency) 88