Séance Séminaire

Séminaire de Probabilités et Statistique

On new multivariate risk measures and its extreme estimators.

Conditional Value-at-Risk (CoVaR) is a risk measure which quantifies the systemic risk in the financial system. Two alternative extensions of the classic univariate CoVaR are proposed in the multivariate setting in this work. A semiparametric procedure and a nonparametric extreme procedure are developed to estimate the new multivariate risk measures. Furthermore, Salvadori, G., De Michele, C. and Durante, F., in "On the return period and design in a multivariate framework" (Hydrology and Earth System Sciences, 15, 3293-3305, 2011) define the multivariate return level as the vector that maximizes a weight function given that the risk vector belongs to a given critical layer of its joint multi- variate distribution function. We provide the explicit expression of the aforementioned multivariate return level and we estimate the measure by using extreme value theory techniques. We study the consistency of the proposed extreme estimators. The performance of the estimators is evaluated on simulated data and on real dataset.