Data-driven generative simulation of SDEs using diffusion models
This work addresses the challenge of simulating SDEs in fields like finance, offering a model-free alternative to traditional methods, though it is incremental as it adapts existing diffusion models to a new application.
This paper tackles the problem of simulating sample paths for unknown stochastic differential equations (SDEs) by introducing a data-driven approach using diffusion models, which generates synthetic paths without requiring explicit drift and diffusion coefficients, and demonstrates its effectiveness in enhancing reinforcement learning for portfolio selection.
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.