A multivariate CVaR risk measure from the perspective of portfolio risk management

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.