Risk Limited Asset Allocation with a Budget Threshold Utility Function and Leptokurtotic Distributions of Returns

ArXiv ID: 2512.11666 “View on arXiv”

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.

Keywords: Asset Allocation, Utility Theory, Budget Threshold Utility, Position Limits, Risk Cost

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: 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.

  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"]