This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the di erent approaches used to construct our measures. We discuss the coherence properties of these multivariate expectiles. Furthermore, we propose a stochastic approximation tool of these risk measures.

In [? ], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent tails, we propose an estimator of extreme multivariate expectiles, in the Fréchet attraction domain case, with asymptotic independence, or for comonotonic margins.

International audienceEuropean insurance sector will soon be faced with the application of the Solvency 2 regulation norms. It will create a real change in the risk management of insurance practices. The ORSA (Own Risk and Solvency Assessment) approach of the second pillar makes the capital allocation an important exercise for all insurers, especially when it comes to groups. Considering multi-branches firms, a capital allocation has to be based on multivariate risk modeling. Several allocation methods are present in the actuarial literature and insurance practices. In this paper, we focus on a risk allocation method. By minimizing some of the multivariate risk indicators, we study the coherence of the risk allocation using an axiomatic approach. Furthermore, we discuss what can be the best allocation choice for an insurance group