Paper: arXiv 2509.03669

Authors: Yu-Jui Huang, Shihao Zhu

Abstract

This paper considers two investors who perform mean-variance portfolio selection with asymmetric information: one knows the true stock dynamics, while the other has to infer the true dynamics from observed stock evolution. Their portfolio selection is interconnected through relative performance concerns, i.e., each investor is concerned about not only her terminal wealth, but how it compares to the average terminal wealth of both investors. We model this as Stackelberg competition: the partially-informed investor (the “follower”) observes the trading behavior of the fully-informed investor (the “leader”) and decides her trading strategy accordingly; the leader, anticipating the follower’s response, in turn selects a trading strategy that best suits her objective. To prevent information leakage, the leader adopts a randomized strategy selected under an entropy-regularized mean-variance objective, where the entropy regularizer quantifies the randomness of a chosen strategy. The follower, on the other hand, observes only the actual trading actions of the leader (sampled from the randomized strategy), but not the randomized strategy itself. Her mean-variance objective is thus a random field, in the form of an expectation conditioned on a realized path of the leader’s trading actions. In the idealized case of continuous sampling of the leader’s trading actions, we derive a Stackelberg equilibrium where the follower’s trading strategy depends linearly on the actual trading actions of the leader and the leader samples her trading actions from Gaussian distributions. In the realistic case of discrete sampling of the leader’s trading actions, the above becomes an $ε$-Stackelberg equilibrium.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a rigorous theoretical framework combining asymmetric information, Stackelberg games, and entropy-regularized mean-variance portfolio selection. While the mathematical formulations and derivations using pathwise HJB systems are deep and highly novel, the paper is purely theoretical and lacks empirical backtesting or real-world data application.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve Mean-Variance Portfolio Selection under Asymmetric Info & Relative Performance] --> B[Input: Market Dynamics, Information Asymmetry & Entropy Regularization]
    B --> C[Model Formulation: Leader-Follower Stackelberg Game]
    
    C --> D[Leader Action: Applies Entropy-Regularized Strategy to Prevent Information Leakage]
    C --> E[Follower Action: Infers True Dynamics from Observed Leader Trades & Stock Evolution]
    
    D --> F[Computational Solving: Continuous vs Discrete Action Sampling]
    E --> F
    
    F --> G[Outcomes: Linear Trading Strategy for Follower, Gaussian Sampling for Leader, & ε-Stackelberg Equilibrium]