Indices of quadratic programs over reproducing kernel Hilbert spaces for fun and profit

ArXiv ID: 2412.18201 “View on arXiv”

Authors: Unknown

Abstract

We give an abstract perspective on quadratic programming with an eye toward long portfolio theory geared toward explaining sparsity via maximum principles. Specifically, in optimal allocation problems, we see that support of an optimal distribution lies in a variety intersect a kind of distinguished boundary of a compact subspace to be allocated over. We demonstrate some of its intelligence by using it to solve mazes and interpret such behavior as the underlying space trying to understand some hypothetical platonic index for which the capital asset pricing model holds.

Keywords: Quadratic Programming, Portfolio Theory, Sparsity, Maximum Principles, Capital Asset Pricing Model, Equities

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats
  • Why: The paper uses highly advanced mathematical concepts like reproducing kernel Hilbert spaces, geometric function theory, and maximum principles in optimal control, which drives a high math complexity score. However, the excerpt focuses on abstract theory, theoretical sparsity explanations, and illustrative toy examples (like coin games and maze solving) without any mention of real backtesting, statistical metrics, or implementation details, resulting in low empirical rigor.
  flowchart TD
    G["Research Goal<br>Understand sparsity via<br>maximum principles in<br>optimal allocation"] --> M["Methodology<br>Indices of Quadratic Programs over<br>Reproducing Kernel Hilbert Spaces RKHS"]
    M --> D["Data / Inputs<br>Maze Environments &<br>Capital Asset Pricing Model CAPI Data"]
    D --> C["Computational Process<br>Maximize quadratic forms subject to<br>support constraints on compact subspaces"]
    C --> O["Key Findings / Outcomes<br>1. Optimal support lies in variety-boundary intersection<br>2. Sparsity explained via maximum principles<br>3. Mazes reveal underlying space dynamics<br>4. Framework interprets hypothetical platonic indices"]
    O --> E((End: Theoretical bridge between<br>QP, geometry, and portfolio theory))