Related papers: DeepSVM: Learning Stochastic Volatility Models wit…
In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic…
Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…
Deep hedging trains neural networks to manage derivative risk under market frictions, but produces hedge ratios with no measure of model confidence -- a significant barrier to deployment. We introduce uncertainty quantification to the deep…
We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between…
We show that differentially private stochastic gradient descent (DP-SGD) can yield poorly calibrated, overconfident deep learning models. This represents a serious issue for safety-critical applications, e.g. in medical diagnosis. We…
Volatility prediction for financial assets is one of the essential questions for understanding financial risks and quadratic price variation. However, although many novel deep learning models were recently proposed, they still have a "hard…
The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…
We devise a novel method for nowcasting implied volatility based on neural operators. Better known as implied volatility smoothing in the financial industry, nowcasting of implied volatility means constructing a smooth surface that is…
Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…
Existing operator learning methods rely on supervised training with high-fidelity simulation data, introducing significant computational cost. In this work, we propose the deep Onsager operator learning (DOOL) method, a novel unsupervised…
Deep Operator Networks (DeepONets) are among the most prominent frameworks for operator learning, grounded in the universal approximation theorem for operators. However, training DeepONets typically requires significant computational…
Despite the increasing availability of high-performance computational resources, Reynolds-Averaged Navier-Stokes (RANS) simulations remain the workhorse for the analysis of turbulent flows in real-world applications. Linear eddy viscosity…
We explore the statistical and economic importance of restrictions on the dynamics of risk compensation from the perspective of a real-time Bayesian learner who predicts bond excess returns using dynamic term structure models (DTSMs). The…
I demonstrate that the conventional seismic full-waveform inversion algorithm can be constructed as a recurrent neural network and so implemented using deep learning software such as TensorFlow. Applying another deep learning concept, the…
In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining…
We propose a predictor-corrector adaptive method for the simulation of hyperbolic partial differential equations (PDEs) on networks under general uncertainty in parameters, initial conditions, or boundary conditions. The approach is based…
We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and…
We consider the problem of training machine learning models on distributed data in a decentralized way. For finite-sum problems, fast single-machine algorithms for large datasets rely on stochastic updates combined with variance reduction.…
A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary value problems described by partial differential equations…
Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…