CV@R penalized portfolio optimization with biased stochastic mirror descent

Manon Costa (), Sébastien Gadat () and Lorick Huang ()
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Manon Costa: IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique
Sébastien Gadat: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Lorick Huang: INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse

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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

Keywords: Stochastic mirror descent; Biased observations; Risk management constraint; Portfolio selection; Discretisation (search for similar items in EconPapers)
Date: 2025-07
Note: View the original document on HAL open archive server: https://hal.science/hal-05147991v1
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Published in Finance and Stochastics, 2025, 29 (3), pp.609-664. ⟨10.1007/s00780-025-00568-2⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05147991

DOI: 10.1007/s00780-025-00568-2

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