I have recently completed a PhD in Actuarial Studies that involved the use of Generalized Linear Models (GLMs) to describe Life Insurance data and I have also taught GLMs to a group of Actuarial Studies students in the context of using them to describe General Insurance (aka non-life insurance or property and casualty insurance) data. From the point of view of a researcher and of an educator, I consider this book to be lacking. To me, "Generalized Linear Models for Insurance Data" feels like a set of lecture notes that would probably make sense if you attended lectures to hear the lecturer explain them, but aren't all that clear to those students who decide to skip class (given that the two authors both teach in universities, there is a good chance that this is, in fact, true).
This book can essentially be divided into two sections: the first 80 pages of the book give the background theory to generalized linear models; and the remaining 116 pages apply this theory to insurance examples. Having worked with GLMs for many years now, the first section of the book made sense to me, but I suspect that a new-comer to this material would find some parts difficult to understand. Very little detail is given on some of the more important topics; no examples are given within this initial section; and concepts that are essentially visual in nature (such as diagnostic plots) are not illustrated with graphs. The second half of the book is an improvement on the first half, with examples and illustrations making up a substantially chunk of the 116 pages. Yet, again, I feel that this section could have benefited by the concepts being discussed in greater detail. From my research and teaching, I know that, for many of these topics, de Jong and Heller have only coasted along the surface of the available information.
Exercises are given at the end of each chapter of this book, and the solutions to these can be found on the books companion website, as can the data sets used throughout this book. Some SAS code for fitting many of the models discussed in the book is given in an appendix at the back of the book, although this code is just for fitting the basic models (not for producing diagnostic plots), and is only really of use if you happen to use SAS (which I don't - I would have preferred R code, which has the advantage of being open-source, so accessible by all).
Author(s): Piet de Jong, Gillian Z. Heller
Series: International series on actuarial science
Publisher: Cambridge University Press
Year: 2008
Language: English
Pages: 208
City: Cambridge; New York
Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
1 Insurance data......Page 13
1.1 Introduction......Page 14
1.2 Types of variables......Page 15
1.3 Data transformations......Page 16
1.4 Data exploration......Page 18
1.5 Grouping and runoff triangles......Page 22
1.6 Assessing distributions......Page 24
1.7 Data issues and biases......Page 25
1.8 Data sets used......Page 26
1.9 Outline of rest of book......Page 31
2.1 Discrete and continuous random variables......Page 32
2.2 Bernoulli......Page 33
2.3 Binomial......Page 34
2.4 Poisson......Page 35
2.5 Negative binomial......Page 36
2.6 Normal......Page 38
2.7 Chi-square and gamma......Page 39
2.8 Inverse Gaussian......Page 41
2.9 Overdispersion......Page 42
Exercises......Page 45
3.1 Exponential family......Page 47
3.2 The variance function......Page 48
3.4 Standard distributions in the exponential family form......Page 49
3.5 Fitting probability functions to data......Page 51
Exercises......Page 53
4.1 History and terminology of linear modeling......Page 54
4.3 Simple linear modeling......Page 55
4.4 Multiple linear modeling......Page 56
4.5 The classical linear model......Page 58
4.7 Weighted least squares......Page 59
4.8 Grouped and ungrouped data......Page 60
4.9 Transformations to normality and linearity......Page 61
4.10 Categorical explanatory variables......Page 63
4.11 Polynomial regression......Page 65
4.12 Banding continuous explanatory variables......Page 66
4.14 Collinearity......Page 67
4.15 Hypothesis testing......Page 68
4.16 Checks using the residuals......Page 70
4.17 Checking explanatory variable specifications......Page 72
4.18 Outliers......Page 73
4.19 Model selection......Page 74
5.1 The generalized linear model......Page 76
5.2 Steps in generalized linear modeling......Page 77
5.4 Offsets......Page 78
5.5 Maximum likelihood estimation......Page 79
5.6 Confidence intervals and prediction......Page 82
5.7 Assessing fits and the deviance......Page 83
5.8 Testing the significance of explanatory variables......Page 86
5.9 Residuals......Page 89
5.10 Further diagnostic tools......Page 91
Exercises......Page 92
6.1 Poisson regression......Page 93
6.2 Poisson overdispersion and negative binomial regression......Page 101
6.3 Quasi-likelihood......Page 106
Exercises......Page 108
7.1 Binary responses......Page 109
7.2 Logistic regression......Page 110
7.3 Application of logistic regression to vehicle insurance......Page 111
7.4 Correcting for exposure......Page 114
7.5 Grouped binary data......Page 117
7.6 Goodness of fit for logistic regression......Page 119
7.7 Categorical responses with more than two categories......Page 122
7.8 Ordinal responses......Page 123
7.9 Nominal responses......Page 128
Exercises......Page 131
8.1 Gamma regression......Page 132
8.2 Inverse Gaussian regression......Page 137
8.3 Tweedie regression......Page 139
Exercises......Page 140
9 Correlated data......Page 141
9.1 Random effects......Page 143
9.2 Specification of within-cluster correlation......Page 148
9.3 Generalized estimating equations......Page 149
Exercise......Page 152
10.1 Generalized additive models......Page 153
10.3 Generalized additive models for location, scale and shape......Page 155
10.4 Zero-adjusted inverse Gaussian regression......Page 157
10.5 A mean and dispersion model for total claim size......Page 160
Exercises......Page 161
Number of children: log link......Page 162
Number of children: identity link......Page 163
Diabetes deaths, categorical age......Page 164
Diabetes deaths, cubic age......Page 166
Third party claims......Page 167
Third party claims......Page 168
Swedish mortality, polynomial age and year......Page 169
A1.3 Quasi-likelihood regression......Page 171
Vehicle insurance: quadratic vehicle value......Page 172
Vehicle insurance: banded vehicle value......Page 173
Vehicle insurance: full model, adjusting for exposure......Page 174
Vehicle insurance: logistic regression on grouped data......Page 176
Proportional odds model......Page 181
Partial proportional odds model......Page 183
A1.6 Nominal regression......Page 187
Personal injury insurance, no adjustment for quickly settled claims......Page 190
Personal injury insurance, with adjustment for quickly settled claims......Page 191
Runoff triangle......Page 192
A1.8 Inverse Gaussian regression......Page 193
A1.9 Logistic regression GLMM......Page 195
A1.10 Logistic regression GEE......Page 197
A1.11 Logistic regression GAM......Page 199
A1.12 GAMLSS......Page 201
A1.13 Zero-adjusted inverse Gaussian regression......Page 202
Bibliography......Page 204
Index......Page 207
