Robust Trading in a Generalized Lattice Market

ArXiv ID: 2310.11023 “View on arXiv”

Authors: Unknown

Abstract

This paper introduces a novel robust trading paradigm, called \textit{“multi-double linear policies”}, situated within a \textit{“generalized”} lattice market. Distinctively, our framework departs from most existing robust trading strategies, which are predominantly limited to single or paired assets and typically embed asset correlation within the trading strategy itself, rather than as an inherent characteristic of the market. Our generalized lattice market model incorporates both serially correlated returns and asset correlation through a conditional probabilistic model. In the nominal case, where the parameters of the model are known, we demonstrate that the proposed policies ensure survivability and probabilistic positivity. We then derive an analytic expression for the worst-case expected gain-loss and prove sufficient conditions that the proposed policies can maintain a \textit{“positive expected profits”}, even within a seemingly nonprofitable symmetric lattice market. When the parameters are unknown and require estimation, we show that the parameter space of the lattice model forms a convex polyhedron, and we present an efficient estimation method using a constrained least-squares method. These theoretical findings are strengthened by extensive empirical studies using data from the top 30 companies within the S&P 500 index, substantiating the efficacy of the generalized model and the robustness of the proposed policies in sustaining the positive expected profit and providing downside risk protection.

Keywords: robust trading, lattice market, probabilistic modeling, constrained least-squares, downside risk

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic modeling, convex optimization, and rigorous proofs (e.g., deriving analytic expressions for worst-case gains), indicating high mathematical complexity. It also includes extensive empirical validation with S&P 500 data and discusses practical implementation details like transaction costs, showing strong empirical rigor.

  flowchart TD
    A["Research Goal: Robust Trading in a Generalized Lattice Market"] --> B["Methodology: Multi-Double Linear Policies"]
    B --> C["Market Model: Generalized Lattice with Serial & Asset Correlation"]
    C --> D{"Parameters Known?"}
    D -- Yes --> E["Analytic Derivation: Worst-case Expected Gain-Loss"]
    D -- No --> F["Constrained Least-Squares Estimation"]
    E --> G["Findings: Survivability & Positive Expected Profit"]
    F --> G
    G --> H["Empirical Validation: S&P 500 Top 30 Companies"]