Related papers: Neural L\'evy SDE for State--Dependent Risk and De…

Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture abrupt, extreme events. While L\'evy stable distributions offer a natural framework for…

Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While L\'evy processes provide a natural mathematical framework for…

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions…

We introduce L\'evy-Flows, a class of normalizing flow models that replace the standard Gaussian base distribution with L\'evy process-based distributions, specifically Variance Gamma (VG) and Normal-Inverse Gaussian (NIG). These…

Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…

We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential L\'evy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time…

Accurate risk assessment is essential for safety-critical autonomous and control systems under uncertainty. In many real-world settings, stochastic dynamics exhibit asymmetric jumps and long-range memory, making long-term risk probabilities…

We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…

Accurately assessing financial risk requires capturing both individual asset volatility and the complex, asymmetric dependence structures that emerge during extreme market events. While modern diffusion-based models have advanced…

This paper proposes a Mixture Density Network specifically designed for forecasting time series that exhibit locally explosive behavior. By incorporating skewed t-distributions as mixture components, our approach offers enhanced flexibility…

We study U.S. Treasury yield curve forecasting under distributional uncertainty and recast forecasting as an operations research and managerial decision problem. Rather than minimizing average forecast error, the forecaster selects a…

This paper investigates an optimal integration of deep learning with financial models for robust asset price forecasting. Specifically, we developed a hybrid framework combining a Long Short-Term Memory (LSTM) network with the Merton-L\'evy…

Multi-step stock price prediction over a long-term horizon is crucial for forecasting its volatility, allowing financial institutions to price and hedge derivatives, and banks to quantify the risk in their trading books. Additionally, most…

Time series driven by unobserved latent states frequently exhibit abrupt jump discontinuities whose timing and magnitude cannot be predicted from observed history alone. Classical jump-diffusion models offer a principled mathematical…

Trust is the invisible glue that holds together the fabric of societies, economic systems, and political institutions. Yet, its dynamics-especially in real-world settings remain unpredictable and difficult to control. While classical trust…

Accurate forecasting of volatility and return quantiles is essential for evaluating financial tail risks such as value-at-risk and expected shortfall. This study proposes an extension of the traditional stochastic volatility model, termed…

Earth system forecasting has traditionally relied on complex physical models that are computationally expensive and require significant domain expertise. In the past decade, the unprecedented increase in spatiotemporal Earth observation…

This manuscript introduces deep learning models that simultaneously describe the dynamics of several yield curves. We aim to learn the dependence structure among the different yield curves induced by the globalization of financial markets…

While deep learning methods have achieved strong performance in time series prediction, their black-box nature and inability to explicitly model underlying stochastic processes often limit their generalization to non-stationary data,…

This paper introduces a novel framework for causal inference in spatial economics that explicitly models the stochastic transition from partial to general equilibrium effects. We develop a Denoising Diffusion Probabilistic Model (DDPM)…