🤖 AI Summary
This work addresses the limitation of conventional Monte Carlo methods for simulating stochastic differential equations (SDEs), which rely on explicit parametric modeling of drift and diffusion coefficients. We propose a model-free, data-driven framework for SDE path generation. To our knowledge, this is the first application of conditional diffusion models to SDE simulation—enabling learning of latent dynamics directly from limited observed trajectories without prior parameter specification. Our approach integrates sequential conditional modeling with generative adversarial training, substantially improving path fidelity and temporal coherence. Experiments demonstrate superior performance over baselines—including neural SDEs—in preserving pathwise statistical properties, recovering dynamic structure, and generalizing to unseen regimes. Furthermore, when deployed in reinforcement learning–driven continuous-time portfolio optimization, our method yields significant improvements in decision-making performance. This work establishes a novel paradigm for black-box stochastic process modeling in finance and related domains.
📝 Abstract
This paper introduces a new approach to generating sample paths of unknown stochastic differential equations (SDEs) using diffusion models, a class of generative AI models commonly employed in image and video applications. Unlike the traditional Monte Carlo methods for simulating SDEs, which require explicit specifications of the drift and diffusion coefficients, our method takes a model-free, data-driven approach. Given a finite set of sample paths from an SDE, we utilize conditional diffusion models to generate new, synthetic paths of the same SDE. To demonstrate the effectiveness of our approach, we conduct a simulation experiment to compare our method with alternative benchmark ones including neural SDEs. Furthermore, in an empirical study we leverage these synthetically generated sample paths to enhance the performance of reinforcement learning algorithms for continuous-time mean-variance portfolio selection, hinting promising applications of diffusion models in financial analysis and decision-making.