CV@R penalized portfolio optimization with biased stochastic mirror descent

Résumé

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.