2024/02/19 by Manon Costa, Costa, Manon, Sébastien Gadat +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #37N40 #60E05 #65C20 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.2402.11999
openalex publication_date 2024/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.