Multivariate geometric expectiles

Klaus Herrmann, Marius Hofert and Mélina Mailhot

Scandinavian Actuarial Journal, 2018, vol. 2018, issue 7, 629-659

Abstract: 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.

Date: 2018
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DOI: 10.1080/03461238.2018.1426038

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