arXiv subjects

Gangnan Yuan

Publications and source records attributed to Gangnan Yuan.

6 recordsLinked to original sources

arXiv2025

Rethinking Nonlinearity: Trainable Gaussian Mixture Modules for Modern Neural Architectures

Neural networks in general, from MLPs and CNNs to attention-based Transformers, are constructed from layers of linear combinations followed by nonlinear operations such as ReLU, Sigmoid, or Softmax. Despite their strength, these conventional designs are often limited in introducing non-linearity by the choice of activation functions. In this work, we introduce Gaussian Mixture-Inspired Nonlinear Modules (GMNM), a new class of differentiable modules that draw on the universal density approximation Gaussian mixture models (GMMs) and distance properties (metric space) of Gaussian kernal. By relaxing probabilistic constraints and adopting a flexible parameterization of Gaussian projections, GMNM can be seamlessly integrated into diverse neural architectures and trained end-to-end with gradient-based methods. Our experiments demonstrate that incorporating GMNM into architectures such as MLPs, CNNs, attention mechanisms, and LSTMs consistently improves performance over standard baselines. These results highlight GMNM's potential as a powerful and flexible module for enhancing efficiency and accuracy across a wide range of machine learning applications.

cs.LG↗

arXiv2025

Hedging with Sparse Reward Reinforcement Learning

Derivatives, as a critical class of financial instruments, isolate and trade the price attributes of risk assets such as stocks, commodities, and indices, aiding risk management and enhancing market efficiency. However, traditional hedging models, constrained by assumptions such as continuous trading and zero transaction costs, fail to satisfy risk control requirements in complex and uncertain real-world markets. With advances in computing technology and deep learning, data-driven trading strategies are becoming increasingly prevalent. This thesis proposes a derivatives hedging framework integrating deep learning and reinforcement learning. The framework comprises a probabilistic forecasting model and a hedging agent, enabling market probability prediction, derivative pricing, and hedging. Specifically, we design a spatiotemporal attention-based probabilistic financial time series forecasting Transformer to address the scarcity of derivatives hedging data. A low-rank attention mechanism compresses high-dimensional assets into a low-dimensional latent space, capturing nonlinear asset relationships. The Transformer models sequential dependencies within this latent space, improving market probability forecasts and constructing an online training environment for downstream hedging tasks. Additionally, we incorporate generalized geometric Brownian motion to develop a risk-neutral pricing approach for derivatives. We model derivatives hedging as a reinforcement learning problem with sparse rewards and propose a behavior cloning-based recurrent proximal policy optimization (BC-RPPO) algorithm. This pretraining-finetuning framework significantly enhances the hedging agent's performance. Numerical experiments in the U.S. and Chinese financial markets demonstrate our method's superiority over traditional approaches.

q-fin.CP↗

arXiv2024

A Gaussian Process Based Method with Deep Kernel Learning for Pricing High-dimensional American Options

In this work, we present a novel machine learning approach for pricing high-dimensional American options based on the modified Gaussian process regression (GPR). We incorporate deep kernel learning and sparse variational Gaussian processes to address the challenges traditionally associated with GPR. These challenges include its diminished reliability in high-dimensional scenarios and the excessive computational costs associated with processing extensive numbers of simulated paths Our findings indicate that the proposed method surpasses the performance of the least squares Monte Carlo method in high-dimensional scenarios, particularly when the underlying assets are modeled by Merton's jump diffusion model. Moreover, our approach does not exhibit a significant increase in computational time as the number of dimensions grows. Consequently, this method emerges as a potential tool for alleviating the challenges posed by the curse of dimensionality.

q-fin.CP↗

arXiv2024

Diffusion Model Conditioning on Gaussian Mixture Model and Negative Gaussian Mixture Gradient

Diffusion models (DMs) are a type of generative model that has a huge impact on image synthesis and beyond. They achieve state-of-the-art generation results in various generative tasks. A great diversity of conditioning inputs, such as text or bounding boxes, are accessible to control the generation. In this work, we propose a conditioning mechanism utilizing Gaussian mixture models (GMMs) as feature conditioning to guide the denoising process. Based on set theory, we provide a comprehensive theoretical analysis that shows that conditional latent distribution based on features and classes is significantly different, so that conditional latent distribution on features produces fewer defect generations than conditioning on classes. Two diffusion models conditioned on the Gaussian mixture model are trained separately for comparison. Experiments support our findings. A novel gradient function called the negative Gaussian mixture gradient (NGMG) is proposed and applied in diffusion model training with an additional classifier. Training stability has improved. We also theoretically prove that NGMG shares the same benefit as the Earth Mover distance (Wasserstein) as a more sensible cost function when learning distributions supported by low-dimensional manifolds.

cs.LG↗

arXiv2023

An Efficient 1 Iteration Learning Algorithm for Gaussian Mixture Model And Gaussian Mixture Embedding For Neural Network

We propose an Gaussian Mixture Model (GMM) learning algorithm, based on our previous work of GMM expansion idea. The new algorithm brings more robustness and simplicity than classic Expectation Maximization (EM) algorithm. It also improves the accuracy and only take 1 iteration for learning. We theoretically proof that this new algorithm is guarantee to converge regardless the parameters initialisation. We compare our GMM expansion method with classic probability layers in neural network leads to demonstrably better capability to overcome data uncertainty and inverse problem. Finally, we test GMM based generator which shows a potential to build further application that able to utilized distribution random sampling for stochastic variation as well as variation control.

cs.LG↗

arXiv2021

Total value adjustment of Bermudan option valuation under pure jump Lévy fluctuations

During the COVID-19 pandemic, many institutions have announced that their counterparties are struggling to fulfill contracts.Therefore, it is necessary to consider the counterparty default risk when pricing options. After the 2008 financial crisis, a variety of value adjustments have been emphasized in the financial industry. The total value adjustment (XVA) is the sum of multiple value adjustments, which is also investigated in many stochastic models such as Heston and Bates models. In this work, a widely used pure jump Lévy process, the CGMY process has been considered for pricing a Bermudan option with various value adjustments. Under a pure jump Lévy process, the value of derivatives satisfies a fractional partial differential equation(FPDE). Therefore, we construct a method which combines Monte Carlo with finite difference of FPDE (MC-FF) to find the numerical approximation of exposure, and compare it with the benchmark Monte Carlo-COS (MC-COS) method. We use the discrete energy estimate method, which is different with the existing works, to derive the convergence of the numerical scheme.Based on the numerical results, the XVA is computed by the financial

math.DS↗