  This article studies and solves the problem of optimal portfolio allocation
with CV@R penalty when dealing with imperfectly simulated financial assets. We
use a Stochastic biased Mirror Descent to find optimal resource allocation for
a portfolio whose underlying assets cannot be generated exactly and may only be
approximated with a numerical scheme that satisfies suitable error bounds,
under a risk management constraint. We establish almost sure asymptotic
properties as well as the rate of convergence for the averaged algorithm. We
then focus on the optimal tuning of the overall procedure to obtain an
optimized numerical cost. Our results are then illustrated numerically on
simulated as well as real data sets.
