| Non-Life Insurance Pricing | p. 1 |
| Rating Factors and Key Ratios | p. 2 |
| Basic Model Assumptions | p. 6 |
| Means and Variances | p. 8 |
| Multiplicative Models | p. 9 |
| The Method of Marginal Totals | p. 11 |
| One Factor at a Time? | p. 12 |
| Exercises | p. 13 |
| The Basics of Pricing with GLMs | p. 15 |
| Exponential Dispersion Models | p. 16 |
| Probability Distribution of the Claim Frequency | p. 18 |
| A Model for Claim Severity | p. 20 |
| Cumulant-Generating Function, Expectation and Variance | p. 21 |
| Tweedie Models | p. 24 |
| The Link Function | p. 26 |
| Canonical Link* | p. 29 |
| Parameter Estimation | p. 30 |
| The Multiplicative Poisson Model | p. 30 |
| General Result | p. 31 |
| Multiplicative Gamma Model for Claim Severity | p. 33 |
| Modeling the Pure Premium | p. 34 |
| Case Study: Motorcycle Insurance | p. 35 |
| Exercises | p. 37 |
| GLM Model Building | p. 39 |
| Hypothesis Testing and Estimation of | p. 39 |
| Pearson's Chi-Square and the Estimation of | p. 42 |
| Testing Hierarchical Models | p. 43 |
| Confidence Intervals Based on Fisher Information | p. 44 |
| Fisher Information | p. 44 |
| Confidence Intervals | p. 45 |
| Numerical Equation Solving* | p. 49 |
| Do the ML Equations Really Give a Maximum?* | p. 50 |
| Asymptotic Normality of the ML Estimators* | p. 51 |
| Residuals | p. 53 |
| Overdispersion | p. 54 |
| Estimation Without Distributional Assumptions | p. 58 |
| Estimating Equations | p. 58 |
| The Overdispersed Poisson Model | p. 60 |
| Denning Deviances from Variance Functions* | p. 60 |
| Miscellanea | p. 61 |
| Model Selection | p. 61 |
| Interaction | p. 62 |
| Offsets | p. 63 |
| Polynomial Regression | p. 63 |
| Large Claims | p. 63 |
| Deductibles* | p. 64 |
| Determining the Premium Level | p. 65 |
| Case Study: Model Selection in MC Insurance | p. 66 |
| Exercises | p. 66 |
| Multi-Level Factors and Credibility Theory | p. 71 |
| The Bühlmann-Straub Model | p. 74 |
| Estimation of Variance Parameters | p. 78 |
| Comparison with Other Notation* | p. 81 |
| Credibility Estimators in Multiplicative Models | p. 81 |
| Estimation of Variance Parameters | p. 84 |
| The Backfitting Algorithm | p. 84 |
| Application to Car Model Classification | p. 86 |
| More than One MLF | p. 87 |
| Exact Credibility* | p. 89 |
| Hierarchical Credibility Models | p. 90 |
| Estimation of Variance Parameters | p. 94 |
| Car Model Classification, the Hierarchical Case | p. 95 |
| Case Study: Bus Insurance | p. 96 |
| Exercises | p. 97 |
| Generalized Additive Models | p. 101 |
| Penalized Deviances | p. 102 |
| Cubic Splines | p. 104 |
| Estimation-One Rating Variable | p. 108 |
| Normal Case | p. 108 |
| Poisson Case | p. 110 |
| Gamma Case | p. 112 |
| Estimation-Several Rating Variables | p. 114 |
| Normal Case | p. 114 |
| Poisson Case | p. 117 |
| Gamma Case | p. 120 |
| Choosing the Smoothing Parameter | p. 121 |
| Interaction Between a Continuous and a Categorical Variable | p. 124 |
| Bivariate Splines | p. 125 |
| Thin Plate Splines | p. 126 |
| Estimation with Thin Plate Splines | p. 127 |
| Case Study: Trying GAMs in Motor Insurance | p. 132 |
| Exercises | p. 133 |
| Some Results from Probability and Statistics | p. 135 |
| The Gamma Function | p. 135 |
| Conditional Expectation | p. 135 |
| The Law of Total Probability | p. 136 |
| Bayes' Theorem | p. 137 |
| Unbiased Estimation of Weighted Variances | p. 138 |
| Some Results on Splines | p. 139 |
| Cubic Splines | p. 139 |
| B-splines | p. 145 |
| Thin Plate Splines | p. 152 |
| Some SAS Syntax | p. 165 |
| Parameter Estimation with Proc Genmod | p. 165 |
| Estimation of and Testing | p. 166 |
| SAS Syntax for Arbitrary Deviance* | p. 167 |
| Backfitting of MLFs | p. 168 |
| Fitting GAMs | p. 68 |
| Miscellanea | p. 168 |
| References | p. 171 |
| Index | p. 173 |
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