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arXiv · 2411.12323

Mirror Descent Algorithms for Risk Budgeting Portfolios

Martin Arnaiz Iglesias·Adil Rengim Cetingoz·Noufel Frikha
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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.

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Martin Arnaiz Iglesias, Adil Rengim Cetingoz, Noufel Frikha. 2024-11-19. Mirror Descent Algorithms for Risk Budgeting Portfolios. https://arxiv.org/abs/2411.12323

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