Abstract

In this thesis, we focus on model combination, incorporating elements of uncertainty quantification to address different actuarial science issues. We first tackle the issue of overconfidence from a single model combination approach, highlighting how different combination assumptions can lead to different conclusions about the predicted variable. This is illustrated with an extreme precipitation example for the regions of Montreal and Quebec. We then focus on Bayesian model averaging (BMA), a very popular model combination technique relying on Bayes' theorem to attribute weights to models based on the likelihood that the observed data comes from the models considered. We propose a correction to the classical expectation-maximisation algorithm to account for data uncertainty, where we assume that the observed data is in fact not the only possible observable data. We then generalise our method to include Dirichlet regression, allowing for combination weights to vary depending on risk characteristics. These BMA approaches are applied to a simulation study as well as a simulated actuarial database and are shown to be very promising, as they allow for a more formal model combination framework for combining actuarial reserving methods in a smooth way based on predictive variables. Next, we adapt Bayesian model averaging using Generalised Likelihood Uncertainty Estimation to extreme value mixture models, and show that this modification allows for identifiying the "best" extreme value threshold, although a combination of models will outperform the single best mixture model. This is illustrated using the Danish reinsurance dataset. Finally, we show that the generalised BMA algorithm can be used to identify flexible extreme value thresholds depending on predictive variables. We use this generalised mixture model combination on a recent dataset from a Canadian automobile insurer.