  A generalization of expectiles for d-dimensional multivariate distribution
functions is introduced. The resulting geometric expectiles are unique
solutions to a convex risk minimization problem and are given by d-dimensional
vectors. They are well behaved under common data transformations and the
corresponding sample version is shown to be a consistent estimator. We
exemplify their usage as risk measures in a number of multivariate settings,
highlighting the influence of varying margins and dependence structures.
