Portfolio optimization under CV@R constraint with stochastic mirror descent

Résumé

This article studies and solves the problem of optimal portfolio allocation with CV@R constraints when dealing with imperfectly simulated nancial assets. We use a Stochastic biased Mirror Descent to nd optimal resource allocation for a portfolio whose underlying assets cannot be generated exactly and may only be approximated with a numerical scheme that satises 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