In this paper, we define a new multivariate conditional Value-at-Risk (MCVaR) risk measure. This MCVaR considers both individual risks and the aggregate risk of a portfolio, but prioritizes the aggregate risk. The new MCVaR risk measure is based on the minimization of the expectation of a multivariate loss function, which balances the shortfall and surplus risks of the aggregate risk and the individual risks in an overall risk of a portfolio. It is shown that the MCVaR risk measure holds the properties of positive homogeneity, translation invariance, subadditivity, and monotonicity under certain conditions. Numerical examples of the MCVaR risk measure are presented to illustrate the effect of dependence among individual risks on the MCVaR.

在本文中，我们定义了一种新的多元条件风险价值 (MCVaR) 风险度量。该 MCVaR 考虑了投资组合的单个风险和总体风险，但优先考虑总体风险。新的 MCVaR 风险度量基于对多元损失函数的期望的最小化，该函数平衡了投资组合整体风险中的总风险和单个风险的短缺和剩余风险。结果表明，MCVaR风险度量在一定条件下具有正同质性、平移不变性、次可加性和单调性等性质。给出了 MCVaR 风险度量的数值示例，以说明个体风险之间的依赖性对 MCVaR 的影响。