Paper: arXiv 2312.10749

Abstract

We focus on a behavioral model, that has been recently proposed in the literature, whose rational can be traced back to the Half-Full/Half-Empty glass metaphor. More precisely, we generalize the Half-Full/Half-Empty approach to the context of positive and negative lotteries and give financial and behavioral interpretations of the Half-Full/Half-Empty parameters. We develop a portfolio selection model based on the Half-Full/Half-Empty strategy, resulting in a nonconvex optimization problem, which, nonetheless, is proven to be equivalent to an alternative Mixed-Integer Linear Programming formulation. By means of the ensuing empirical analysis, based on three real-world datasets, the Half-Full/Half-Empty model is shown to be very versatile by appropriately varying its parameters, and to provide portfolios displaying promising performances in terms of risk and profitability, compared with Prospect Theory, risk minimization approaches and Equally-Weighted portfolios.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents advanced mathematical modeling with nonconvex optimization and Mixed-Integer Linear Programming (MILP) formulations, showing high mathematical density. It includes empirical analysis on three real-world datasets with comparative performance metrics against established benchmarks, indicating substantial data and implementation requirements.

Research Flowchart

  flowchart TD
  A["Research Goal: Develop & Test<br>Half-Full/Half-Empty<br>Portfolio Selection Model"] --> B["Generalize HFHE Approach<br>to Positive & Negative Lotteries"]
  B --> C["Formulate Optimization Problem<br>Nonconvex Objective"]
  C --> D{"Convert to MILP<br>for Solvability"}
  D --> E["Empirical Validation<br>3 Real-World Datasets"]
  E --> F["Comparative Analysis<br>vs Prospect Theory, Risk Min, EW"]
  F --> G["Key Findings: Versatile Model<br>Risk/Profitability Improvements<br>Validated MILP Equivalence"]