A Weissman-type estimator of the conditional marginal expected shortfall

Yuri Goegebeur (1) , Armelle Guillou (2) , Nguyen Khanh Le Ho (1) , Jing Qin (1)

1 IMADA - Department of Mathematics and Computer Science [Odense]
2 IRMA - Institut de Recherche Mathématique Avancée

The marginal expected shortfall is an important risk measure in finance and actuarial science, which has been extended recently to the case where the random variables of main interest are observed together with a covariate. This leads to the concept of conditional marginal expected shortfall for which an estimator is proposed allowing extrapolation outside the data range. The main asymptotic properties of this estimator have been established, using empirical processes arguments combined with the multivariate extreme value theory. The finite sample behavior of the proposed estimator is evaluated with a simulation experiment, and the practical applicability is illustrated on vehicle insurance customer data.

Mots clés: extrapolation; Conditional marginal expected shortfall; Pareto-type distribution

Domaines: Statistiques [math.ST]

Yuri Goegebeur, Armelle Guillou, Nguyen Khanh Le Ho, Jing Qin. A Weissman-type estimator of the conditional marginal expected shortfall. Econometrics and Statistics , In press, ⟨10.1016/j.ecosta.2021.09.006⟩. ⟨hal-02613135v4⟩