On Robustness of Double Linear Policy with Time-Varying Weights

Paper: arXiv 2303.10806

Authors: Xin-Yu Wang, Chung-Han Hsieh

Abstract

In this paper, we extend the existing double linear policy by incorporating time-varying weights instead of constant weights and study a certain robustness property, called robust positive expectation (RPE), in a discrete-time setting. We prove that the RPE property holds by employing a novel elementary symmetric polynomials characterization approach and derive an explicit expression for both the expected cumulative gain-loss function and its variance. To validate our theory, we perform extensive Monte Carlo simulations using various weighting functions. Furthermore, we demonstrate how this policy can be effectively incorporated with standard technical analysis techniques, using the moving average as a trading signal.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 4.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically solid extension to the double linear policy using elementary symmetric polynomials to prove the robust positive expectation property. However, its empirical section relies heavily on Monte Carlo simulations and basic moving average signals rather than rigorous historical market backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate Robust Positive Expectation for Time-Varying Double Linear Policy] --> B[Model Formulation: Incorporate Time-Varying Weights in Discrete-Time Setting]
    B --> C[Theoretical Analysis: Elementary Symmetric Polynomials Characterization]
    C --> D[Derived Analytical Outcomes: Explicit Cumulative Gain-Loss Function & Variance]
    D --> E[Empirical Validation: Monte Carlo Simulations & Technical Analysis Signal Strategy]
    E --> F[Key Outcome: Proven RPE Property & Practical Trading Application]