Univariate and multivariate risk measures

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The proposed research program aims at analyzing mathematical properties of risk measures, and their extensions to higher dimensions. The general objectives are the following: first, to analyze properties of univariate risk measures, and to extend them to dynamic models, and to study possible applications either to financial portfolio, or to actuarial risks. Secondly, to study multivariate extensions, including a more systematic analysis of standard multivariate copulas (and more specifically those based on mu-quantile), and a statistical analysis of multivariate risk measure estimation. Finally, applications of multivariate risks measures will be investigated, and more specifically axiomatic of capital allocation, with a particular interest to multi-period dynamic allocations.