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

TL;DR

This paper introduces a novel abstract framework for quadratic programming in reproducing kernel Hilbert spaces, connecting portfolio optimization, sparsity, and fundamental financial models through geometric and boundary analysis.

Contribution

It provides a new perspective on quadratic programming in RKHS, linking optimal support, boundary behavior, and financial theories like CAPM.

Findings

Support of optimal distributions lies on a distinguished boundary.

The approach can solve maze-like problems illustrating boundary behavior.

Interprets financial models through geometric and boundary analysis.

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.