{"ID":2849219,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.24607","arxiv_id":"2510.24607","title":"Entropy-Guided Multiplicative Updates: KL Projections for Multi-Factor Target Exposures","abstract":"We introduce Entropy-Guided Multiplicative Updates (EGMU), a convex optimization framework for constructing multi-factor target-exposure portfolios by minimizing Kullback-Leibler divergence from a benchmark under linear factor constraints. We establish feasibility and uniqueness of strictly positive solutions when the benchmark and targets satisfy convex-hull conditions. We derive the dual concave formulation with explicit gradient, Hessian, and sensitivity expressions, and provide two provably convergent solvers: a damped dual Newton method with global convergence and local quadratic rate, and a KL-projection scheme based on iterative proportional fitting and Bregman-Dykstra projections. We further generalize EGMU to handle elastic targets and robust target sets, and introduce a path-following ordinary differential equation for tracing solution trajectories. Stable and scalable implementations are provided using LogSumExp stabilization, covariance regularization, and half-space KL projections. Our focus is on theory and reproducible algorithms; empirical benchmarking is optional.","short_abstract":"We introduce Entropy-Guided Multiplicative Updates (EGMU), a convex optimization framework for constructing multi-factor target-exposure portfolios by minimizing Kullback-Leibler divergence from a benchmark under linear factor constraints. We establish feasibility and uniqueness of strictly positive solutions when the...","url_abs":"https://arxiv.org/abs/2510.24607","url_pdf":"https://arxiv.org/pdf/2510.24607v2","authors":"[\"Yimeng Qiu\"]","published":"2025-10-28T16:36:09Z","proceeding":"q-fin.PM","tasks":"[\"q-fin.PM\",\"math.OC\"]","methods":"[]","has_code":false}