Paper: arXiv 2510.24607

Authors: Yimeng Qiu

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is dense with advanced mathematical derivations, including convex optimization, sensitivity analysis, and ODE-based path-following, while explicitly stating that empirical benchmarking is optional and providing only theoretical algorithms without real-world data or backtests.

Research Flowchart

  flowchart TD
  A["Research Goal: Construct multi-factor target-exposure portfolios"]
  B["Methodology: Entropy-Guided Multiplicative Updates EGMU Framework"]
  C["Input: Benchmark & Target Exposures"]
  D["Solver 1: Damped Dual Newton Method"]
  E["Solver 2: Bregman-Dykstra KL Projections"]
  F["Generalization: Elastic Targets & Robust Sets"]
  G["Key Findings: Uniqueness, Convergence, Stability"]

  A --> B
  C --> B
  B --> D
  B --> E
  B --> F
  D & E & F --> G