Portfolio Analysis Based on Markowitz Stochastic Dominance Criteria: A Behavioral Perspective

ArXiv ID: 2509.22896 “View on arXiv”

Authors: Peng Xu

Abstract

This paper develops stochastic optimization problems for describing and analyzing behavioral investors with Markowitz Stochastic Dominance (MSD) preferences. Specifically, we establish dominance conditions in a discrete state-space to capture all reverse S-shaped MSD preferences as well as all subjective decision weights generated by inverse S-shaped probability weighting functions. We demonstrate that these dominance conditions can be admitted as linear constraints into the stochastic optimization problems to formulate computationally tractable mixed-integer linear programming (MILP) models. We then employ the developed MILP models in financial portfolio analysis and examine classic behavioral factors such as reference point and subjective probability distortion in behavioral investors’ portfolio decisions.

Keywords: Markowitz Stochastic Dominance (MSD), Mixed-integer linear programming (MILP), Inverse S-shaped probability weighting, Behavioral portfolio theory, Reverse S-shaped preferences, Portfolio Management

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats
  • Why: The paper is highly mathematical, featuring advanced stochastic optimization, stochastic dominance theory, and detailed proofs leading to MILP formulations. However, its empirical section appears limited to applying the derived models to financial data for behavioral factor analysis, with no mention of actual backtesting, performance metrics, or implementation details, placing it in the research/lab phase.
  flowchart TD
    A["Research Goal:<br/>Model Behavioral Portfolio Decisions<br/>using Markowitz Stochastic Dominance (MSD)"] --> B["Methodology:<br/>Develop Stochastic Optimization with<br/>MSD Constraints"]
    B --> C["Data/Input:<br/>Asset Returns with Subjective<br/>Probability Weighting"]
    C --> D["Computational Process:<br/>Formulate as Mixed-Integer<br/>Linear Programming (MILP)"]
    D --> E["Analysis:<br/>Simulate Portfolio Choices<br/>varying Reference Points & Probability Distortions"]
    E --> F["Key Findings/Outcomes:<br/>1. Validated Reverse S-shaped Preferences<br/>2. Quantified Impact of Reference Points<br/>3. Demonstrated Tractable MILP for<br/>Behavioral Portfolio Theory"]