A study of the fundamentals of actuarial economic models
This thesis examines the methods that have been used by actuaries to describe and model the economic variables required for actuarial calculations. Traditionally actuaries have only used average future values to describe these variables and they have tended to use relatively informal methods for determining these averages. These informal methods are potentially subject to numerous biases. The likelihood of these biases occurring could be reduced by using the more formal methods of financial economics and stochastic modelling. Stochastic models also provide additional information that is essential for some applications. The main UK stochastic asset models that are considered include: Wilkie's (1995b) model, Dyson and Exley's (1995) expectations model, and Smith's (1996) jumpequilibrium model. Wilkie's model was developed primarily from data considerations, whilst the other two models were developed from theoretical considerations. Wilkie's model is shown to be inconsistent with the rational expectations hypothesis, the efficient market hypothesis, and aspects of portfolio theory. Dyson and Exley's model is shown to be inconsistent with portfolio theory. The jump-equilibrium model is consistent with most financial theories, but it is shown to produce returns with moments that are inconsistent with historical data. The importance of these limitations is then examined from a methodological perspective. This review emphasises the importance and difficulty of empirical testing. It also suggests that economic predictive success is always likely to be limited. As a result, it is argued that a model's pragmatic qualities are relatively more important than they would otherwise be, that a theoretical framework is invaluable for motivating economic models and for directing research activities, and that actuaries should aim to develop models with shorter time horizons. The empirical adequacy of financial economic theories is then examined and many persistent problems are reported. Despite these problems it is suggested that financial economics provides a useful theoretical framework. Lastly, the empirical adequacy of Wilkie's model is considered using the criteria of Hendry's (1995) general-to-specific approach. This review identifies some apparent weaknesses. In particular, the out-of-sample residuals from Wilkie's (1986a) model do not seem to be independent.