Summary

In this chapter we reformulate the survival model introduced in Chapter 2 as an example of a multiple state model. We then introduce several other multiple state models which are useful as models for different types of life insurance policies. A general definition of a multiple state model, together with assumptions and notation, is given in Section 8.3. In Section 8.4 we discuss the derivation of formulae for probabilities and in Section 8.5 the numerical evaluation of these probabilities. This is extended in Section 8.6 to premium calculation and in Section 8.7 to the numerical evaluation of policy values.

In the final three sections we study in more detail some specific multiple state models that are particularly useful – a multiple decrement model, the joint life and last survivor model and a model where transitions can take place at specified ages.

Examples of multiple state models

Multiple state models are one of the most exciting developments in actuarial science in recent years. They are a natural tool for many important areas of practical interest to actuaries. They also simplify and provide a sound foundation for some traditional actuarial techniques. In this section we illustrate some of the uses of multiple state models using a number of examples which are common in actuarial practice.