Portfolio optimization under CV@R constraint with stochastic mirror descent

Manon Costa (1) , Sébastien Gadat (2, 3) , Lorick Huang (4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 TSE-R - Toulouse School of Economics
3 IUF - Institut universitaire de France
4 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse

This article studies and solves the problem of optimal portfolio allocation with CV@R constraints 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.

Mots clés: Stochastic Mirror Descent; Biased observations; Risk management constraint; Portfolio selection; Discretization

Domaines: Statistiques [math.ST]; Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Manon Costa, Sébastien Gadat, Lorick Huang. Portfolio optimization under CV@R constraint with stochastic mirror descent. 2022. ⟨hal-03697232v1⟩