Introduction

Insurance requires modelling tools different from those of the preceding chapter. Pension schemes and life insurance make use of lifecycle descriptions. Individuals start as ‘active’ (paying contributions), at one point they ‘retire’ (drawing benefits) or become ‘disabled’ (benefits again) and they may die. Stochastic models are needed to keep track of what happens, but they cannot be constructed by means of linear relationships like those in the preceding chapter. There are no numerical variables to connect! Distributions are used instead.

The central concept is conditional probabilities and distributions, expressing mathematically that what has occurred is going to influence (but not determine) what comes next. That idea is the principal topic of the chapter. As elsewhere, mathematical aspects (here going rather deep) are downplayed for the conditional viewpoint as a modelling tool. Sequences of states in lifecycles involve time series (but of a different kind from those in Chapter 5) and are treated in Section 6.6. Actually, time may not be involved at all. Risk heterogeneity in property insurance is a typical (and important) example. Consider a car owner. What he encounters daily in the traffic is influenced by randomness, but so is (from a company point of view) his ability as a driver. These are uncertainties of entirely different origin and define a hierarchy (driver comes first). Conditional modelling is the natural way of connecting random effects operating on different levels like this. The same viewpoint is used when errors due to estimation and Monte Carlo are examined in the next chapter, and there are countless other examples.