NMAK15018U Modelling Dependence in Non-Life Insurance (AAM)

Knowledge: At the end of the course the student should know how to incorporate dependency into their 
statistical analysis of insurance data. They should understand that the main cause of risk is 
individual, but groups of risk may be subject to some common factors that can explain a certain portion 
of  the total risk. They will have knowledge about:

Linear mixed model(LMM).  This is the usual linear regression model with the addition of so-called 
random effects. The purpose of the random effects is to account for intra-dependence in the data, 
so that for example all policies in one group can be subject to the same random factor.

Generalized linear mixed model(GLMM). As the name says this is a generalization of the generalized 
linear models(GLM), in that it also includes random effects. Although theoretically not very difficult, 
finding good parameters is a numerical challenge, but the student will learn how to use existing 
software for this purpose.

Empirical Bayes, or mixture, models. The  students will learn how these can be generated, and 
how they incorparate dependence. This is a  different approach to dependence than LMM and GLMM, 
but it is useful to be aware of both approaches.

Credibility models. Finally, the students will known something about credibility models, and 
how credibility is related to LMM and special cases of empirical Bayes. These are robust and 
simple to fit, but lacks in theoretical structure.

Skills: The students should develop the necessary theoretical skills to understand the consequences 
of the various models. They are supposed to be able to know the pros and cons of each model, and 
be able to make a judicious choice in a practical situation. They will also know how to estimate 
models in R, either by using existing programs, or by writing their own programs if no suitable 
program exists.

Competencies. The students should be able to  translate their specific data problems into a workable 
model, and be able to estimate unknown parameters and compare various models in order to pick a 
suitable one, weighting simplicity against generality.