Paper: arXiv 2512.11666

Authors: Graham L Giller

Abstract

An analytical solution to single-horizon asset allocation for an investor with a piecewise-linear utility function, called herein the “budget threshold utility,” and exogenous position limits is presented. The resulting functional form has a surprisingly simple structure and can be readily interpreted as representing the addition of a simple “risk cost” to otherwise frictionless trading.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a heavy analytical derivation using advanced mathematical concepts like Gamma functions and generalized error distributions, but lacks empirical validation beyond theoretical discussion and a proposed constant for backtesting.

Research Flowchart

  flowchart TD
  A["Research Goal: Analytical solution for asset allocation<br>with budget threshold utility & position limits"] --> B["Methodology: Mean-Variance Optimization<br>with piecewise-linear utility constraints"]
  B --> C["Data Inputs: Asset return distributions<br>including leptokurtotic/fat-tailed"]
  C --> D["Computational Process: Derive first-order conditions<br>and solve for optimal portfolio weights"]
  D --> E["Key Finding: Simple analytical solution<br>representing risk cost added to frictionless trading"]
  E --> F["Outcome: Practical framework for<br>risk-limited asset allocation"]