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CV@R penalized portfolio optimization with biased stochastic mirror descent

Author

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  • Gadat, Sébastien
  • Costa, Manon
  • Huang, Lorick

Abstract

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.

Suggested Citation

  • Gadat, Sébastien & Costa, Manon & Huang, Lorick, 2022. "CV@R penalized portfolio optimization with biased stochastic mirror descent," TSE Working Papers 22-1342, Toulouse School of Economics (TSE), revised Nov 2023.
    • Handle: RePEc:tse:wpaper:127041
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    References listed on IDEAS

    as
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    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
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    4. Laruelle Sophie & Pagès Gilles, 2012. "Stochastic approximation with averaging innovation applied to Finance," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 1-51, January.
    5. Frikha, N. & Huang, L., 2015. "A multi-step Richardson–Romberg extrapolation method for stochastic approximation," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4066-4101.
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    More about this item

    Keywords

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