多元风险的共单调测度
Comonotonic measures of multivariate risks
摘要：
我们提出了一个著名的特征的多元扩展S。作为最大相关泛函的正则和相干风险测度的Kusuoka。这涉及到通过广义分位数函数将同单调性的概念扩展到随机向量。此外，我们建议取代目前的法律不变性，次可加性和共单调性公理的等价属性，我们称之为强连贯性，我们认为有更自然的经济解释。最后，我们重新制定的计算定期和连贯的风险措施作为一个最优运输问题，我们提供了一个算法和实现。
英文摘要：
We propose a multivariate extension of a well-known characterization by S. Kusuoka of regular and coherent risk measures as maximal correlation functionals. This involves an extension of the notion of comonotonicity to random vectors through generalized quantile functions. Moreover, we propose to replace the current law invariance, subadditivity and comonotonicity axioms by an equivalent property we call strong coherence and that we argue has more natural economic interpretation. Finally, we reformulate the computation of regular and coherent risk measures as an optimal transportation problem, for which we provide an algorithm and implementation.
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