A folding methodology for multivariate extremes: estimation of the spectral probability measure and actuarial applications

Abstract

In this paper, the folding methodology developed in the context of univariate Extreme Value Theory (EVT) by You et al. is extended to a multivariate framework. Under the usual EVT assumption of regularly varying tails, our multivariate folding allows for the estimation of the spectral probability measure. A new weakly consistent estimator based on the classical empirical estimator is proposed. Its behaviour is illustrated through simulations and an actuarial application relative to reinsurance pricing in the case of an insurance data-set.

Keywords:

• extreme value theory
• folding
• multivariate regular variation
• spectral probability measure
• point processes
• reinsurance pricing

Acknowledgments

Part of this work was supported by the FP7 ACQWA project, the GIS MOPERA project and by the ANR PEPER project. The authors are grateful to Johan Segers for providing the MELE R routine. The authors would like to thank an anonymous referee for valuable suggestions, which lead to an improved version of the article.