Mirror Descent Algorithms for Risk Budgeting Portfolios
Portfolio Management
2024-11-20 v1 Probability
Risk Management
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
Cite
@article{arxiv.2411.12323,
title = {Mirror Descent Algorithms for Risk Budgeting Portfolios},
author = {Martin Arnaiz Iglesias and Adil Rengim Cetingoz and Noufel Frikha},
journal= {arXiv preprint arXiv:2411.12323},
year = {2024}
}