  We present a framework for constructing multivariate risk measures that is
inspired from univariate Optimized Certainty Equivalent (OCE) risk measures. We
show that this new class of risk measures verifies the desirable properties
such as convexity, monotonocity and cash invariance. We also address numerical
aspects of their computations using stochastic algorithms instead of using
Monte Carlo or Fourier methods that do not provide any error of the estimation.
