Mirror Descent Algorithms for Risk Budgeting Portfolios

Martin Arnaiz Iglesias, Adil Rengim Cetingoz and Noufel Frikha
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Martin Arnaiz Iglesias: UP1 UFR27
Adil Rengim Cetingoz: UP1 UFR27
Noufel Frikha: UP1 UFR27

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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.

Date: 2024-11
New Economics Papers: this item is included in nep-cmp and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2411.12323

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