The need for diagnostic assessment of bootstrap predictive models
Glen Barnett and Ben Zehnwirth
Contents:
- The need for diagnostic assessment of bootstrap predictive models
- A basic bootstrap introduction
- Diagnostic displays for a bootstrapped chain ladder
- Assessing bootstrap predictive distributions
- Some other considerations
- Conclusions
- References
- Appendices
The following set of pages are available as a PDF document here.
Some other considerations
All chain-ladder reproducing models (including both the quasi-Poisson GLM and the Mack model) must assume that the variance of the losses is proportional to the mean (or they will necessarily fail to reproduce the chain ladder). This assumption is found to be rarely tenable in practice - and for an obvious reason. While it can make sense with claim counts - for example, if the counts are higher on average they also tend to be more spread but often with lower coefficient of variation. If they happen to be Poisson-distributed (a strong assumption), the variance will be specifically proportional to the mean. However, heterogeneity or dependence in claim probabilities can make it untenable even for claim numbers. But with claim payments, the amount paid on each claim is itself a random variable, not a constant, and anything that makes the claim payments variable will make the variation increase faster than the mean. Simple variation in claim size (such as a constant percentage change, whether due to inflation effects or change in mix of business or any number of other effects) will make the variance increase as the square of the mean, while claim size effects that vary from policy to policy can make it increase still faster. Dependence in claim size effects across policies can make it increase faster again. Consequently the chain ladder assumption of variance proportional to mean must be viewed with a great deal of caution, and carefully checked.
The chain ladder model is overparameterized. It assumes, for example, that there is no information in nearby development periods about the level of payments in a given development, yet the development generally follows a fairly smooth trend - indicating that there is information there, and that the trend could be described with few parameters. This overparameterization leads to unstable forecasts.
Finally, in respect of the bootstrap, the sample statistic may in some circumstances be very inefficient as an estimator of the corresponding population quantities. It would be prudent to check that it makes sense to use the estimator you have in mind for distributions that would plausibly describe the data.
Continue with: Conclusions.
