Chapter Preview. As explained in more detail in Volume I of this book, multilevel modeling represents a powerful tool that recently gained popularity in actuarial research. It builds on recent findings linking credibility theory in actuarial science to the linear mixed model in statistics. In this chapter, we present a practical application of multilevel modeling in dealing with the complex nature of group health insurance policies within a ratemaking context. In particular, using a real dataset from one of the major insurance companies in Egypt, we illustrate how the pure premiums for these policies can be estimated using both these advanced models and traditional (single-level) general linear models. The results are compared using both in-sample goodness of fit tests and out-of-sample validation.
The overall aim is to illustrate the additional advantages gained by using these advanced types of models, more specifically, its ability to allow for the complex data structures underlying group health insurance policies. These include, for example, multidimensional benefit packages and panel/longitudinal aspects, which are often necessary for experience rating purposes.
Interested readers may refer to Chapters 2, 7, 8, and 9 in Volume I of this book for more detail regarding the models used in this chapter.
Motivation and Background
Motivation behind this research can be attributed to four main factors: (1) the difficulties associated with insurance ratemaking in general; (2) the complex nature of group health insurance policies in particular; (3) the high potential for multilevel modeling to handle this complexity; and (4) the importance of this application for the Egyptian market context. Each of these factors is considered in more detail in the following subsections.
Adequate ratemaking represents a continuous concern for most actuaries worldwide. This is due to its significant impact on the profitability and sustainability of insurance business. It also reflects the distinctive nature of this business as opposed to other types of business. For example, in general the true cost of issuing a particular insurance policy is usually not known with certainty at time of sale, as it depends on future uncertain claims. This is different from most other types of products, where all production costs are usually known prior to sale (Werner and Modlin, 2010). Accordingly, calculating suitable rates for insurance products is usually not an easy process. In fact, it is often described as combining art with science (see, e.g., McClenahan, 2001).