Paper: arXiv 2501.14259

Abstract

In financial markets, agents often mutually influence each other’s investment strategies and adjust their strategies to align with others. However, there is limited quantitative study of agents’ investment strategies in such scenarios. In this work, we formulate the optimal investment differential game problem to study the mutual influence among agents. We derive the analytical solutions for agents’ optimal strategies and propose a fast algorithm to find approximate solutions with low computational complexity. We theoretically analyze the impact of mutual influence on agents’ optimal strategies and terminal wealth. When the mutual influence is strong and approaches infinity, we show that agents’ optimal strategies converge to the asymptotic strategy. Furthermore, in general cases, we prove that agents’ optimal strategies are linear combinations of the asymptotic strategy and their rational strategies without others’ influence. We validate the performance of the fast algorithm and verify the correctness of our analysis using numerical experiments. This work is crucial to comprehend mutual influence among agents and design effective mechanisms to guide their strategies in financial markets.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced mathematical methods, including optimal control theory, differential games, stochastic calculus, and matrix algebra to derive analytical solutions, indicating high math complexity. However, the empirical validation is limited to numerical experiments with low computational complexity, and lacks real-world data, backtests, or implementation details, resulting in low empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal: Quantify mutual<br>influence on investment strategies"] --> B["Formulate Differential Game<br>Model"]

  B --> C["Derive Analytical Solutions<br>Optimal Strategies"]
  B --> D["Propose Fast Algorithm<br>Low Complexity Approximation"]

  C --> E["Theoretical Analysis"]
  D --> E

  E --> F["Key Findings:<br>1. Convergence to Asymptotic Strategy<br>2. Linear Combination Structure<br>3. Impact of Influence Strength"]
  
  C --> G["Numerical Experiments"]
  D --> G
  F --> G
  
  style A fill:#e1f5fe
  style F fill:#e8f5e8

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2 of 95 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.