arXiv subjects

Jiale Zha

Publications and source records attributed to Jiale Zha.

3 recordsLinked to original sources

arXiv2025

Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimization

We propose a novel conditional diffusion model for contextual portfolio optimization that learns the cross-sectional distribution of next-day stock returns conditioned on high-dimensional asset-specific factors. Our model leverages a Diffusion Transformer architecture with token-wise conditioning, which enables linking each asset's return to its own factor vector while capturing complex cross-asset dependencies. By drawing generative samples from the learned conditional return distribution, we perform daily mean-variance and mean-CVaR optimization, incorporating transaction costs and realistic constraints. Using data from the Chinese A-share market, we demonstrate that our approach consistently outperforms various standard benchmarks across multiple risk-adjusted performance metrics. Furthermore, we establish a 2-Wasserstein error bound for the conditional diffusion model and quantify how its distributional approximation errors propagate to the downstream portfolio optimization task. Our results demonstrate the potential of generative diffusion models for high-dimensional, risk-sensitive contextual stochastic optimization and financial decision making.

q-fin.PM↗

arXiv2025

Generating solution paths of Markovian stochastic differential equations using diffusion models

This paper introduces a new approach to generating sample paths of unknown Markovian stochastic differential equations (SDEs) using diffusion models, a class of generative AI methods 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, ours 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. Numerical experiments show that our method consistently outperforms two alternative methods in terms of the Kullback--Leibler (KL) divergence between the distributions of the target SDE paths and the generated ones. Moreover, we present a theoretical error analysis deriving an explicit bound on the said KL divergence. Finally, in simulation and empirical studies, we leverage these synthetically generated sample paths to boost the performance of reinforcement learning algorithms for continuous-time mean--variance portfolio selection, hinting promising applications of our study in financial analysis and decision-making.

cs.LG↗

arXiv2024

Reward-Directed Score-Based Diffusion Models via q-Learning

We propose a new reinforcement learning (RL) formulation for training continuous-time score-based diffusion models for generative AI to generate samples that maximize reward functions while keeping the generated distributions close to the unknown target data distributions. Different from most existing studies, ours does not involve any pretrained model for the unknown score functions of the noise-perturbed data distributions, nor does it attempt to learn the score functions. Instead, we formulate the problem as entropy-regularized continuous-time RL and show that the optimal stochastic policy has a Gaussian distribution with a known covariance matrix. Based on this result, we parameterize the mean of Gaussian policies and develop an actor--critic type (little) q-learning algorithm to solve the RL problem. A key ingredient in our algorithm design is to obtain noisy observations from the unknown score function via a ratio estimator. Our formulation can also be adapted to solve pure score-matching and fine-tuning pretrained models. Numerically, we show the effectiveness of our approach by comparing its performance with two state-of-the-art RL methods that fine-tune pretrained models on several generative tasks including high-dimensional image generations. Finally, we discuss extensions of our RL formulation to probability flow ODE implementation of diffusion models and to conditional diffusion models.

cs.LG↗