Solving dynamic portfolio selection problems via score-based diffusion models

ArXiv ID: 2507.09916 “View on arXiv”

Authors: Ahmad Aghapour, Erhan Bayraktar, Fengyi Yuan

Abstract

In this paper, we tackle the dynamic mean-variance portfolio selection problem in a {"\it model-free"} manner, based on (generative) diffusion models. We propose using data sampled from the real model $\mathbb P$ (which is unknown) with limited size to train a generative model $\mathbb Q$ (from which we can easily and adequately sample). With adaptive training and sampling methods that are tailor-made for time series data, we obtain quantification bounds between $\mathbb P$ and $\mathbb Q$ in terms of the adapted Wasserstein metric $\mathcal A W_2$. Importantly, the proposed adapted sampling method also facilitates {"\it conditional sampling"}. In the second part of this paper, we provide the stability of the mean-variance portfolio optimization problems in $\mathcal A W _2$. Then, combined with the error bounds and the stability result, we propose a policy gradient algorithm based on the generative environment, in which our innovative adapted sampling method provides approximate scenario generators. We illustrate the performance of our algorithm on both simulated and real data. For real data, the algorithm based on the generative environment produces portfolios that beat several important baselines, including the Markowitz portfolio, the equal weight (naive) portfolio, and S&P 500.

Keywords: Mean-Variance Portfolio Selection, Diffusion Models, Adapted Wasserstein Metric, Model-Free, Policy Gradient, Multi-Asset / Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical machinery including score-based diffusion models, adapted Wasserstein metrics, and SDE stability analysis, while also providing empirical validation on both simulated and real financial data with performance comparisons against established baselines.

  flowchart TD
    A["Research Goal: Solve Dynamic Mean-Variance Portfolio Selection model-free"] --> B["Methodology: Score-based Diffusion Models & Policy Gradient"]
    B --> C["Data Inputs: Real Market Data (Limited Size)"]
    C --> D["Computation: Train Generative Model Q via Adapted Sampling"]
    D --> E["Computation: Approximate Scenario Generators & Optimize Portfolio"]
    E --> F["Outcomes: Error Bounds (Adapted Wasserstein) & Portfolio Stability"]
    F --> G["Findings: Algorithm beats Markowitz, Equal Weight, and S&P 500"]