Non-Life Insurance: Statistical
Techniques and Data Analytics
(6414M0327Y)
2022-2023
Lecture Notes
1/60
,2/60
,Modern Actuarial Risk Theory (MART)
Formularium ........................................................................................................................................... 5
9 Generalized Linear Models .................................................................................................................. 7
9.1 Linear Regression / Transformation .............................................................................................. 9
9.2 Generalized Linear Models (Nelder & Wedderburn, 1972) ........................................................ 14
9.3 GLMs and four traditional estimation methods .......................................................................... 18
9.4 Deviance and scaled deviance .................................................................................................... 27
9.5 Analyzing a simple automobile portfolio (Appendix A.3) ........................................................... 33
9.6 Analyzing a bonus-malus system for a large portfolio using GLM .............................................. 36
10 IBNR techniques ............................................................................................................................... 38
10.1 Introduction .............................................................................................................................. 39
10.2 Two, time-honored IBNR methods ........................................................................................... 40
10.3 A GLM that encompasses various IBNR methods ..................................................................... 43
10.4 Illustration of some IBNR methods ........................................................................................... 44
10.5 Solving IBNR problems by R ...................................................................................................... 47
10.6 Variability of the IBNR estimate ................................................................................................ 51
10.7 An IBNR-problem with information on known exposures ........................................................ 53
8 Credibility Theory (Bayes) .................................................................................................................. 55
8.5 Negative binomial model for the number of car insurance claims ............................................. 56
3/60
, 4/60
Techniques and Data Analytics
(6414M0327Y)
2022-2023
Lecture Notes
1/60
,2/60
,Modern Actuarial Risk Theory (MART)
Formularium ........................................................................................................................................... 5
9 Generalized Linear Models .................................................................................................................. 7
9.1 Linear Regression / Transformation .............................................................................................. 9
9.2 Generalized Linear Models (Nelder & Wedderburn, 1972) ........................................................ 14
9.3 GLMs and four traditional estimation methods .......................................................................... 18
9.4 Deviance and scaled deviance .................................................................................................... 27
9.5 Analyzing a simple automobile portfolio (Appendix A.3) ........................................................... 33
9.6 Analyzing a bonus-malus system for a large portfolio using GLM .............................................. 36
10 IBNR techniques ............................................................................................................................... 38
10.1 Introduction .............................................................................................................................. 39
10.2 Two, time-honored IBNR methods ........................................................................................... 40
10.3 A GLM that encompasses various IBNR methods ..................................................................... 43
10.4 Illustration of some IBNR methods ........................................................................................... 44
10.5 Solving IBNR problems by R ...................................................................................................... 47
10.6 Variability of the IBNR estimate ................................................................................................ 51
10.7 An IBNR-problem with information on known exposures ........................................................ 53
8 Credibility Theory (Bayes) .................................................................................................................. 55
8.5 Negative binomial model for the number of car insurance claims ............................................. 56
3/60
, 4/60
