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Guillou, Armelle; Naveau, Philippe; You, Alexandre

A folding methodology for multivariate extremes: estimation of the spectral probability measure and actuarial applications. (English) Zbl 1401.62209

Scand. Actuar. J. 2015, No. 7, 549-572 (2015).
Summary: In this paper, the folding methodology developed in the context of univariate extreme value theory (EVT) by A. You et al. [J. Stat. Plann. Inference 140, No. 7, 1775–1787 (2010; Zbl 1184.62075)] 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.

Cited in 1 Document

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62M15 Inference from stochastic processes and spectral analysis
91B30 Risk theory, insurance (MSC2010)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G70 Extreme value theory; extremal stochastic processes

Keywords:

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

Citations:

Zbl 1184.62075
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Full Text: DOI HAL

References:

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