Mirror Descent Algorithms for Risk Budgeting Portfolios

• 成果类型: Article; Early Access
• 署名作者: Iglesias, Martin Amaiz; Cetingoz, Adil Rengim; Frikha, Noufel
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0847
• 发表日期: 2026-04-07
• 关键词: risk budgeting; Risk measures; mirror descent; Monte Carlo; numerical finance; Value-at-risk; stochastic-approximation; parity

摘要

This paper introduces and examines numerical approximation schemes for computing risk budgeting portfolios associated to positive homogeneous and subadditive 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 nonasymptotic 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.