Apr 2015-Mar 2016

Math-Fi seminar on 28 Mar

2016.03.23 Wed up
  • Date : 28 Mar. (Mon.)
  • Place: W.W. 7th-floor, 4th lab.
  • Time : 16:30-18:00
  • Speaker: Marie Kratz (ESSEC, Paris)
  • Title: On Risk Concentration
  • Abstract: 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, Singapore). 

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