1.1 The Model-Based Approach
The model-based approach should be considered in the context of the objectives of any given problem. Many problems in actuarial science involve the building of a mathematical model that can be used to forecast or predict insurance costs in the future.
A model is a simplified mathematical description that is constructed based on the knowledge and experience of the actuary combined with data from the past. The data guide the actuary in selecting the form of the model as well as in calibrating unknown quantities, usually called parameters. The model provides a balance between simplicity and conformity to the available data.
The simplicity is measured in terms of such things as the number of unknown parameters (the fewer the simpler); the conformity to data is measured in terms of the discrepancy between the data and the model. Model selection is based on a balance between the two criteria, namely, fit and simplicity.
1.1.1 The Modeling Process
The modeling process is illustrated in Figure 1.1, which describes the following six stages:
- Stage 1 One or more models are selected based on the analyst's prior knowledge and experience, and possibly on the nature and form of the available data. For example, in studies of mortality, models may contain covariate information such as age, sex, duration, policy type, medical information, and lifestyle variables. In studies of the size of an insurance loss, a statistical distribution (e.g. lognormal, ...