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Mirror Descent Algorithms for Risk Budgeting Portfolios

Author

Listed:
  • Martin Arnaiz Iglesias

    (UP1 UFR27)

  • Adil Rengim Cetingoz

    (UP1 UFR27)

  • Noufel Frikha

    (UP1 UFR27)

Abstract

This paper introduces and examines numerical approximation schemes for computing risk budgeting portfolios associated to positive homogeneous and sub-additive risk measures. We employ Mirror Descent algorithms to determine the optimal risk budgeting weights in both deterministic and stochastic settings, establishing convergence along with an explicit non-asymptotic quantitative rate for the averaged algorithm. A comprehensive numerical analysis follows, illustrating our theoretical findings across various risk measures -- including standard deviation, Expected Shortfall, deviation measures, and Variantiles -- and comparing the performance with that of the standard stochastic gradient descent method recently proposed in the literature.

Suggested Citation

  • Martin Arnaiz Iglesias & Adil Rengim Cetingoz & Noufel Frikha, 2024. "Mirror Descent Algorithms for Risk Budgeting Portfolios," Papers 2411.12323, arXiv.org.
    • Handle: RePEc:arx:papers:2411.12323
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    File URL: http://arxiv.org/pdf/2411.12323
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