Solving dynamic portfolio selection problems via score-based diffusion models

• URL: http://arxiv.org/abs/2507.09916v2
• Date: Mon, 21 Jul 2025 05:00:13 GMT
• Title: Solving dynamic portfolio selection problems via score-based diffusion models
• Authors: Ahmad Aghapour, Erhan Bayraktar, Fengyi Yuan,
• Abstract summary: We tackle the dynamic mean-variance portfolio selection problem in a it model-free manner, based on (generative) diffusion models.<n>We propose using data sampled from the real model $mathbb P$ with limited size to train a generative model $mathbb Q$.<n>With adaptive training and sampling methods that are tailor-made for time series data, we obtain bounds between $mathbb P$ and $mathbb Q$.
• Score: 3.8857791305699565
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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