Dynamic data generation and dynamic portfolio selection: an application of a score-based diffusion model

Abstract

We study dynamic data generation and its application to model-free dynamic portfolio selection. Existing score-based diffusion models are typically designed to learn a static data distribution, whereas dynamic decision problems require generated trajectories that preserve the sequential information structure of the underlying process and support conditional sampling. To address this gap, we develop an adaptive score-based diffusion framework for dynamic data. Given samples from an unknown data-generating model $\mathbb P$, the framework learns a generative model $\mathbb Q$ through conditional score matching and generates trajectories sequentially by updating the conditioning information over time. We establish quantitative error bounds between $\mathbb P$ and $\mathbb Q$ under the adapted Wasserstein metric $\mathcal A\mathcal W_2$, which is tailored to nonanticipative dynamic problems, and show that the same adaptive sampling scheme provides conditional path generators. We then apply this dynamic data generation framework to dynamic mean-variance portfolio selection with limited historical price data. We prove stability of the dynamic mean-variance problem with respect to $\mathcal A\mathcal W_2$, thereby translating the generative approximation error into performance control for portfolio policies. Building on these results, we implement a policy-gradient algorithm in the learned generative environment, where adaptively sampled paths serve as training scenarios. A synthetic ARMA experiment shows that the proposed adaptive sampling scheme generates distributions close to the true data-generating process. On real market data, the proposed approach outperforms several benchmarks, including the Markowitz portfolio, the equal-weight portfolio, and the S\&P 500.