Solving dynamic portfolio selection problems via score-based diffusion models

2025-07-14

AI Summary

This paper addresses the dynamic mean-variance portfolio selection problem and proposes the first fully model-free solution framework. Methodologically, it constructs a generative environment based on score-based diffusion models, enabling conditional sampling and time-series modeling; introduces an adaptive Wasserstein metric to establish the first theoretical error bounds between the generated and true market distributions, along with guarantees on policy stability; and designs a policy gradient algorithm operating within this generative environment. Key contributions include: (i) the integration of generative modeling with dynamic stochastic optimization; (ii) verifiable distributional approximation guarantees without assuming parametric forms for asset returns; and (iii) elimination of reliance on prior knowledge of return distributions. Empirical evaluation demonstrates that the proposed method significantly outperforms the Markowitz model, equal-weighted portfolios, and the S&P 500 index on both synthetic and real-world financial market data.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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 $mathcal P$ (which is unknown) with limited size to train a generative model $mathcal Q$ (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 $mathcal P$ and $mathcal Q$ 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.

Problem

• Dynamic mean-variance portfolio selection without model assumptions
• Training generative models for limited real financial data
• Stable portfolio optimization using adaptive sampling methods

Innovation

• Score-based diffusion models for portfolio selection
• Adaptive training for time series data
• Policy gradient algorithm with generative environment