CV@R-penalised portfolio optimisation with biased stochastic mirror descent

This article studies and solves the problem of optimal portfolio allocation with a 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 optimised numerical cost. Our results are illustrated numerically on simulated as well as on real data sets.