In this paper, we study the close relationship between multivariate coherent and convex risk measures. Namely, starting from a multivariate convex risk measure, we propose a family of multivariate coherent risk measures induced by it. In return, the convex risk measure can be represented by its induced coherent risk measures. The representation result for the induced coherent risk measures is given in terms of the minimal penalty function of the convex risk measure. Finally, an example is also given.

中文翻译：

---

多元凸风险测度诱发的多元相干风险测度

在本文中，我们研究了多元连贯和凸风险测度之间的密切关系。即，从多元凸风险度量开始，我们提出了由其引发的一系列多元相干风险度量。作为回报，凸风险度量可以用其诱发的相干风险度量来表示。诱导相干风险度量的表示结果以凸风险度量的最小罚函数给出。最后，给出一个例子。