A folding methodology for multivariate extremes: estimation of the spectral probability measure and actuarial applications |
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| Authors: | Armelle Guillou Philippe Naveau Alexandre You |
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| Institution: | 1. IRMA, UMR 7501, Université de Strasbourg et CNRS, Strasbourg cedex, France.armelle.guillou@math.unistra.fr;3. Laboratoire des Sciences du Climat et de l’Environnement, LSCE-IPSL-CNRS, Gif-sur-Yvette, France.;4. Société Générale Insurance – Sogessur, Paris, France. |
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| 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. |
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| Keywords: | extreme value theory folding multivariate regular variation spectral probability measure point processes reinsurance pricing |
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