Predictive Modeling Applications in Actuarial Science
- Volume 1
- Introduction
- Predictive Modeling Foundations
- Predictive Modeling Methods
- Bayesian and Mixed Modeling
- Longitudinal Modeling
- Volume 2
- Generalized Linear Model
- Extensions of the Generalized Linear Model
- Unsupervised Predictive Modeling Methods
-
Applications on Current Problems in Actuarial Science
- Chapter 8 - The Predictive Distribution of Loss Reserve Estimates over a Finite Time Horizon
- Chapter 9 - Finite Mixture Model and Workers’ Compensation Large-Loss Regression Analysis
- Chapter 10 - A Framework for Managing Claim Escalation Using Predictive Modeling
- Chapter 11 - Predictive Modeling for Usage-Based Auto Insurance
Chapter 9 - Credibility and Regression Modeling
Authors
Vytaras Brazauskas | University of Wisconsin - Milwaukee
vytaras@uwm.edu
Harald Dornheim | KPMG AG Switzerland
bavaria_harry@gmx.de
Ponmalar Ratnam | University of Wisconsin - Milwaukee
psratnam@uwm.edu
Chapter Preview
This chapter introduces the reader to credibility and related regression modeling. The first section provides a brief overview of credibility theory, regression-type credibility, and discusses historical developments. The next section shows how some well-known credibility models can be embedded within the linear mixed model framework. Specific procedures on how such models can be used for prediction and standard ratemaking are given as well. Further, in Section 9.3, a step-by-step numerical example, based on the widely-studied Hachemeister's data, is developed to illustrate the methodology. All computations are done using the statistical software package R. The fourth section identifies some practical issues with the standard methodology. In particular, its lack of robustness against various types of outliers is mentioned. Possible solutions that have been proposed in the statistical and actuarial literatures are discussed. Performance of the most effective proposals is illustrated on the Hachemeister's data set and compared to that of the standard methods. Suggestions for further reading are made in Section 9.5.
| Data | R Code |
| How to read a dataset | Hachem Revised |