(Non-Parametric) Bootstrap Robust Optimization for Portfolios and Trading Strategies

ArXiv ID: 2510.12725 “View on arXiv”

Authors: Daniel Cunha Oliveira, Grover Guzman, Nick Firoozye

Abstract

Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances demands methods that mitigate estimation error, parameter instability, and model misspecification. Traditional approaches, including parametric, bootstrap-based, and Bayesian methods, enhance stability by relying on confidence intervals or probabilistic priors but often impose restrictive assumptions. This study introduces a non-parametric bootstrap framework for robust optimization in financial decision-making. By resampling empirical data, the framework constructs flexible, data-driven confidence intervals without assuming specific distributional forms, thus capturing uncertainty in statistical estimates, model parameters, and utility functions. Treating utility as a random variable enables percentile-based optimization, naturally suited for risk-sensitive and worst-case decision-making. The approach aligns with recent advances in robust optimization, reinforcement learning, and risk-aware control, offering a unified perspective on robustness and generalization. Empirically, the framework mitigates overfitting and selection bias in trading strategy optimization and improves generalization in portfolio allocation. Results across portfolio and time-series momentum experiments demonstrate that the proposed method delivers smoother, more stable out-of-sample performance, offering a practical, distribution-free alternative to traditional robust optimization methods.

Keywords: Robust Optimization, Non-Parametric Bootstrap, Portfolio Optimization, Uncertainty Quantification, Risk-Aware Control, Portfolio/General Asset Allocation

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper introduces a novel non-parametric bootstrap framework for robust optimization, involving complex statistical and optimization theory, and provides empirical results across portfolio and time-series momentum experiments, demonstrating out-of-sample performance improvement.

  flowchart TD
    Start["Research Goal: Develop a robust framework for portfolio optimization under uncertainty without parametric assumptions"] --> Inputs["Data Inputs: Empirical financial time-series data<br/>Uncertain parameters: Returns, Covariances, Utility"]
    Inputs --> Method["Methodology: Non-Parametric Bootstrap<br/>Resample data to construct flexible confidence intervals<br/>Treat utility as a random variable"]
    Method --> Process["Computational Process:<br/>Percentile-based robust optimization<br/>(Minimize worst-case outcome/Maximize lower percentile utility)"]
    Process --> Outcomes["Key Findings: <br/>1. Mitigates overfitting & selection bias<br/>2. Improves out-of-sample generalization<br/>3. Delivers stable, smooth portfolio performance"]