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 - Université Paris 1 Panthéon-Sorbonne - UFR Mathématiques & Informatique - UP1 - Université Paris 1 Panthéon-Sorbonne
Adil Rengim Cetingoz: UP1 UFR27 - Université Paris 1 Panthéon-Sorbonne - UFR Mathématiques & Informatique - UP1 - Université Paris 1 Panthéon-Sorbonne
Noufel Frikha: UP1 UFR27 - Université Paris 1 Panthéon-Sorbonne - UFR Mathématiques & Informatique - UP1 - Université Paris 1 Panthéon-Sorbonne

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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.

Keywords: Risk Budgeting risk measures Mirror Descent Monte Carlo numerical finance 65C05 62L20 62G32 91Gxx; Risk Budgeting; risk measures; Mirror Descent; Monte Carlo; numerical finance; numerical finance 65C05; 62L20; 62G32; 91Gxx (search for similar items in EconPapers)
Date: 2024-11-18
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