A hierarchical Bayesian model is proposed to quantify the magnitude of extreme surges on the Atlantic coast of Canada with limited data. Generalized extreme value distributions are fitted to surges derived from water levels measured at 21 buoys along the coast. The parameters of these distributions are linked together through a Gaussian field whose mean and variance are driven by atmospheric sea‐level pressure and the distance between stations, respectively. This allows for information sharing across the original stations and for interpolation anywhere along the coast. The use of a copula at the data level of the hierarchy further accounts for the dependence between locations, allowing for inference beyond a site‐by‐site basis. It is shown how the extreme surges derived from the model can be combined with the tidal process to predict potentially catastrophic water levels.

This paper focuses on semi-parametric estimation of multivariate expectiles for extreme levels of risk. Multivariate expectiles and their extremes have been the focus of plentiful research in recent years. In particular, it has been noted that due to the difficulty in estimating these values for elevated levels of risk, an alternative formulation of the underlying optimization problem would be necessary. However, in such a scenario, estimators have only been provided for the limiting cases of tail dependence: independence and comonotonicity. In this paper, we extend the estimation of multivariate extreme expectiles (MEEs) by providing a consistent estimation scheme for random vectors with any arbitrary dependence structure. Specifically, we show that if the upper tail dependence function, tail index, and tail ratio can be consistently estimated, then one would be able to accurately estimate MEEs. The finite-sample performance of this methodology is illustrated using both simulated and real data.

In this paper, we address the estimation of multivariate value-at-risk (VaR) and tail value-at-risk (TVaR). We recall definitions for the bivariate lower and upper orthant VaR and bivariate lower and upper orthant TVaR, presented in Cossette et al. [Eur. Actuar. J. 3 (2013) 321–357 or Methodol. Comput. Appl. Probab. (2014) 1–22]. Here, we present estimators for both these measures extended to an arbitrary dimension d ≥ 2 and establish the consistency of our estimator for the lower and upper orthant TVaR in any dimension. We demonstrate these results by providing numerical examples that compare our estimator to theoretical results for both simulated and real data.