| Přispěvatelé: |
Department of Mathematics and Computer Science [Odense] (IMADA), University of Southern Denmark (SDU), Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), Guillou, Armelle |
| Popis: |
Several risk measures have been proposed in the literature, among them the marginal mean excess, defined as MME_p = \mathbb E[(Y^{(1)}-Q_1(1-p))_+|Y^{(2)}> Q_{2}(1-p)], provided \mathbb E|Y^{(1)}|< \infty, where (Y^{(1)}, Y^{(2)}) denotes a pair of risk factors, y_+:=\max(0,y), Q_j the quantile function of Y^{(j)}, j=1, 2, and p\in (0,1). In this paper we consider a generalization of this measure, where the random variables of main interest (Y^{(1)},Y^{(2)}) are observed together with a random covariate X \in \mathbb R^d, and where the Y^{(1)} excess is also power transformed. This leads to the concept of conditional marginal excess moment 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 estimator is evaluated by a simulation experiment. We apply also our method on a vehicle insurance customer dataset. |
