Reinforcement Learning for Financial Index Tracking

ArXiv ID: 2308.02820 “View on arXiv”

Authors: Unknown

Abstract

We propose the first discrete-time infinite-horizon dynamic formulation of the financial index tracking problem under both return-based tracking error and value-based tracking error. The formulation overcomes the limitations of existing models by incorporating the intertemporal dynamics of market information variables not limited to prices, allowing exact calculation of transaction costs, accounting for the tradeoff between overall tracking error and transaction costs, allowing effective use of data in a long time period, etc. The formulation also allows novel decision variables of cash injection or withdraw. We propose to solve the portfolio rebalancing equation using a Banach fixed point iteration, which allows to accurately calculate the transaction costs specified as nonlinear functions of trading volumes in practice. We propose an extension of deep reinforcement learning (RL) method to solve the dynamic formulation. Our RL method resolves the issue of data limitation resulting from the availability of a single sample path of financial data by a novel training scheme. A comprehensive empirical study based on a 17-year-long testing set demonstrates that the proposed method outperforms a benchmark method in terms of tracking accuracy and has the potential for earning extra profit through cash withdraw strategy.

Keywords: Index Tracking, Deep Reinforcement Learning (DRL), Banach Fixed Point Iteration, Transaction Cost Modeling, Dynamic Programming, Equities

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including Banach fixed point iteration, infinite-horizon dynamic programming, and deep RL theory, while also presenting a comprehensive 17-year empirical study with transaction cost modeling and benchmark comparisons.

  flowchart TD
    A["Research Goal<br>Formulate Dynamic<br>Index Tracking Problem"] --> B["Data & Setup<br>17-Year Equity Data<br>Transactions Costs"]
    B --> C{"Core Methodology"}
    C --> D["Dynamic Formulation<br>Infinite-Horizon RL<br>Cash Injection/Withdraw"]
    C --> E["Banach Fixed Point<br>Iterative Solver"]
    D --> F["RL Algorithm<br>Training Scheme<br>Data Augmentation"]
    E --> G["Computational Process<br>Estimate Costs &<br>Optimize Portfolio"]
    F --> G
    G --> H["Key Findings & Outcomes<br>1. Outperforms Benchmarks<br>2. Lower Tracking Error<br>3. Extra Profit via Cash"]