Robo-Advising in Motion: A Model Predictive Control Approach

ArXiv ID: 2601.09127 “View on arXiv”

Authors: Tomasz R. Bielecki, Igor Cialenco

Abstract

Robo-advisors (RAs) are automated portfolio management systems that complement traditional financial advisors by offering lower fees and smaller initial investment requirements. While most existing RAs rely on static, one-period allocation methods, we propose a dynamic, multi-period asset-allocation framework that leverages Model Predictive Control (MPC) to generate suboptimal but practically effective strategies. Our approach combines a Hidden Markov Model with Black-Litterman (BL) methodology to forecast asset returns and covariances, and incorporates practically important constraints, including turnover limits, transaction costs, and target portfolio allocations. We study two predominant optimality criteria in wealth management: dynamic mean-variance (MV) and dynamic risk-budgeting (MRB). Numerical experiments demonstrate that MPC-based strategies consistently outperform myopic approaches, with MV providing flexible and diversified portfolios, while MRB delivers smoother allocations less sensitive to key parameters. These findings highlight the trade-offs between adaptability and stability in practical robo-advising design.

Keywords: Model Predictive Control, Hidden Markov Model, Black-Litterman, Dynamic Risk-Budgeting, Robo-advising, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical techniques including Model Predictive Control, Hidden Markov Models, and Black-Litterman estimations, with rigorous derivations and stochastic calculus. It includes detailed numerical experiments with market data, comparing dynamic vs. myopic strategies and analyzing performance metrics like turnover, sensitivity, and transaction costs.

  flowchart TD
    A["Research Goal:<br/>Dynamic Multi-Period<br/>Robo-Advising Framework"] --> B["Methodology:<br/>MPC, HMM, &<br/>Black-Litterman"]
    B --> C{"Optimality Criteria"}
    C --> D["Dynamic Mean-Variance<br/>MV"]
    C --> E["Dynamic Risk-Budgeting<br/>MRB"]
    D & E --> F["Constraints & Inputs:<br/>Turnover, Costs,<br/>Asset Returns/Covariances"]
    F --> G["Key Findings"]
    G --> H["MV: Flexible,<br/>Diversified Portfolios"]
    G --> I["MRB: Smoother,<br/>Parameter-Insensitive"]
    G --> J["MPC Outperforms<br/>Myopic Approaches"]