A Discussion of Parameter and Model Uncertainty in Insurance

In this paper we consider the process of modelling uncertainty. In particular we are concerned with making inferences about some quantity of interest which, at present, has been unobserved. Examples of such a quantity include the probability of ruin of a surplus process, the accumulation of an investment, the level or surplus or deficit in a pension fund and the future volume of new business in an insurance company. Uncertainty in this quantity of interest, y, arises from three sources: • uncertainty due to the stochastic nature of a given model; • uncertainty in the values of the parameters in a given model; • uncertainty in the model underlying what we are able to observe and determining the quantity of interest. It is common in actuarial science to find that the first source of uncertainty is the only one which receives rigorous attention. A limited amount of research in recent years has considered the effect of parameter uncertainty, while there is still considerable scope for development of methods which deal in a balanced way with model risk. Here we discuss a methodology which allows all three sources of uncertainty to be assessed in a more coherent fashion.