Mirror Descent Algorithms for Risk Budgeting Portfolios
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909395673153536 |
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| author | Iglesias, Martin Arnaiz Cetingoz, Adil Rengim Frikha, Noufel |
| author_facet | Iglesias, Martin Arnaiz Cetingoz, Adil Rengim Frikha, Noufel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mirror Descent Algorithms for Risk Budgeting Portfolios Iglesias, Martin Arnaiz Cetingoz, Adil Rengim Frikha, Noufel Portfolio Management Probability Risk Management 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. |
| title | Mirror Descent Algorithms for Risk Budgeting Portfolios |
| topic | Portfolio Management Probability Risk Management |
| url | https://arxiv.org/abs/2411.12323 |