Optimal Investment with Herd Behaviour Using Rational Decision Decomposition

ArXiv ID: 2401.07183 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we study the optimal investment problem considering the herd behaviour between two agents, including one leading expert and one following agent whose decisions are influenced by those of the leading expert. In the objective functional of the optimal investment problem, we introduce the average deviation term to measure the distance between the two agents’ decisions and use the variational method to find its analytical solution. To theoretically analyze the impact of the following agent’s herd behaviour on his/her decision, we decompose his/her optimal decision into a convex linear combination of the two agents’ rational decisions, which we call the rational decision decomposition. Furthermore, we define the weight function in the rational decision decomposition as the following agent’s investment opinion to measure the preference of his/her own rational decision over that of the leading expert. We use the investment opinion to quantitatively analyze the impact of the herd behaviour, the following agent’s initial wealth, the excess return, and the volatility of the risky asset on the optimal decision. We validate our analyses through numerical experiments on real stock data. This study is crucial to understanding investors’ herd behaviour in decision-making and designing effective mechanisms to guide their decisions.

Keywords: Herd Behaviour, Rational Decision Decomposition, Variational Method, Optimal Investment, Expert-Follower Model, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 5.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic optimal control (variational methods, integrals, analytical solutions) and heavy LaTeX/formulas, indicating high mathematical complexity. It validates analyses via numerical experiments on real stock data, but lacks detailed implementation/backtest specifications, placing it in the middle-high empirical rigor range.

  flowchart TD
    A["Research Goal<br>Quantify Herd Behaviour Impact<br>on Optimal Investment Decisions"] --> B{"Methodology"}
    
    B --> C["Model Setup<br>Expert-Follower 2-Agent Model"]
    B --> D["Optimization Problem<br>Minimize Risk + Herd Deviation<br>Variational Method"]
    B --> E["Rational Decision Decomposition<br>Follower's Decision = w * Own Rational + (1-w) * Expert's Rational"]
    
    C --> F["Data & Inputs<br>Real Stock Data<br>Excess Return, Volatility, Wealth"]
    D --> F
    E --> F
    
    F --> G["Computation & Analysis<br>Derive Analytical Solution<br>Calculate Weight Function 'w'<br>Numerical Experiments"]
    
    G --> H["Key Findings/Outcomes<br>Herding Reduces Risk Exposure<br>'w' Quantifies Preference<br>Validated with Real Data"]