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

Author

Listed:
  • Manon Costa

    (Université Paul Sabatier)

  • Sébastien Gadat

    (Institut Universitaire de France and Toulouse School of Economics, CNRS UMR 5314)

  • Lorick Huang

    (Université de Toulouse)

Abstract

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.

Suggested Citation

  • Manon Costa & Sébastien Gadat & Lorick Huang, 2025. "CV@R-penalised portfolio optimisation with biased stochastic mirror descent," Finance and Stochastics, Springer, vol. 29(3), pages 609-664, July.
    • Handle: RePEc:spr:finsto:v:29:y:2025:i:3:d:10.1007_s00780-025-00568-2
    DOI: 10.1007/s00780-025-00568-2
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    References listed on IDEAS

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    Keywords

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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