  Recent advances in extreme value theory have established $\ell$-Pareto
processes as the natural limits for extreme events defined in terms of
exceedances of a risk functional. Here we provide methods for the practical
modelling of data based on a tractable yet flexible dependence model. We
introduce the class of elliptical $\ell$-Pareto processes, which arise as the
limit of threshold exceedances of certain elliptical processes characterized by
a correlation function and a shape parameter. An efficient inference method
based on maximizing a full likelihood with partial censoring is developed.
Novel procedures for exact conditional and unconditional simulation are
proposed. These ideas are illustrated using precipitation extremes in
Switzerland.
