Univariate and multivariate risk measures

建议的研究计划的目的是分析风险措施的数学性质，并将其扩展到更高的维度。 本文的总体目标是：首先，分析单变量风险度量的性质，并将其推广到动态模型，研究其在金融投资组合中的应用， 或精算风险。 其次，研究多变量扩展，包括标准多变量Copula（更具体地说，基于μ分位数的Copula）的更系统的分析，以及多变量风险度量估计的统计分析。 最后，将研究多变量风险度量的应用，更具体地说，研究资本配置的公理化，特别关注多期动态配置。

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.