Speaker: Prof. Marie Kratz, ESSEC Business School, CREAR (risk research center)
Date: 26 October 2015
Time: 2:15 - 3:15 p.m.
Venue: Lecture Hall I, Department of Mathematics
We study the local behavior of (extreme) quantiles of the sum of heavy-tailed random variables, to infer on risk concentration. Looking at the literature, asymptotic (for high threshold) results have been obtained when assuming (asymptotic) independence and second order regularly varying conditions on the variables. Other asymptotic results have been obtained in the dependent case when considering specific copula structures. Our contribution is to investigate on one hand, the non-asymptotic case (i.e. for any threshold), providing analytical results on the risk concentration for copula models that are used in practice, and comparing them with results obtained via Monte-Carlo method. On the other hand, when looking at extreme quantiles, we assume a multivariate second order regular variation condition on the vectors and provide asymptotic risk concentration results. We show that many models used in practice come under the purview of such an assumption and provide a few examples. Moreover this ties up related results available in the literature under a broad umbrella. This presentation is based on two joint works, one with M. Dacorogna and L. Elbahtouri (SCOR), the other with B. Das (SUTD).