Machine learning methods perform well in prediction tasks within the range of the training data. When interest is in quantiles of the response that go beyond the observed records, these methods typically break down. Extreme value theory provides the mathematical foundation for estimation of such extreme quantiles. A common approach is to approximate the exceedances over a high threshold by the generalized Pareto distribution. For conditional extreme quantiles, one may model the parameters of this distribution as functions of the predictors. Up to now, the existing methods are either not flexible enough or do not generalize well in higher dimensions. We develop new approaches for extreme quantile regression that estimate the parameters of the generalized Pareto distribution with tree-based methods and recurrent neural networks. Our estimators outperform classical machine learning methods and methods from extreme value theory in simulations studies. We illustrate how the recurrent neural network model can be used for effective forecasting of flood risk.

Extreme value statistics is essentially concerned with the modelling of rare events which are hard to predict and occur with only little warning. In this talk, I will address a number of challenges highlighted in the literature and how these align with the domain of attraction characterisation for extremes. Such a characterisation stems from a suite of mildly restrictive conditions, qualitative in nature, which not only provide computational convenience but also furnish sharp approximations to asymptotically justified models for extreme values, a key aspect to statistical testing procedures as well as interval estimation methodology in a nonparametric setting.

Expectiles were originally introduced by Newey and Powell (Econometrica 1987) in order to test for symmetry in heteroskedastic regression models. They have recently seen a regain of interest due to nice properties they have in the context of risk assessment in insurance and finance. I will discuss the definition of expectiles, some of their most important properties, and recent work around their estimation and inference at extreme levels. I will illustrate the results on actuarial and financial data.