Search Results (132)

Stock return prediction for quantitative trading in U.S. equity markets has evolved from parametric econometric modeling toward data-driven deep learning systems that must jointly capture temporal dynamics, discontinuous jumps, and evolving cross-asset dependencies. Existing approaches still face three key challenges in deep learning-based stock return prediction: jump-aware temporal modeling is often missing or handled by ad hoc heuristics; higher-order stock relations are frequently encoded by static graphs/hypergraphs that do not adapt across market conditions, and temporal and relational learning are commonly implemented as sequential blocks with limited bidirectional interaction. We propose LévyHyper, an end-to-end framework that unifies jump-aware temporal encoding with regime-adaptive dynamic hypergraph learning and multi-scale hypergraph reasoning. LévyHyper integrates a neural jump-aware temporal layer motivated by Lévy jump-diffusion modeling, a regime-weighted fusion of predefined and learned hyperedges via a differentiable constructor, and a multi-scale hypergraph convolution module for hierarchical temporal aggregation. Experiments on S&P 500 data (463 stocks, 10 evaluation phases, prediction horizon $\tau =5$ trading days) show that LévyHyper improves IC/RankIC and portfolio-level Sharpe ratio over strong baselines on average. We additionally report uncertainty estimates, significance tests, and transaction-cost sensitivity to support robust conclusions. Full article

We study a hybrid stochastic SIS co-infection model for two primary strains and a co-infected class with Crowley–Martin incidence, Markovian regime switching, and Lévy jumps. The model is a four-dimensional regime-switching Lévy-driven SDE system with state-dependent diffusion and jump coefficients. Under natural integrability conditions on the jumps and a mild structural assumption on removal rates, we prove uniform high-order moment bounds for the total population, establish pathwise sublinear growth, and derive strong laws of large numbers for all Brownian and Lévy martingales, reducing the long-time analysis to deterministic time averages. Using logarithmic Lyapunov functionals for the infective classes, we introduce four noise-corrected effective growth parameters ${\lambda }_1,\dots ,{\lambda }_4$ and two interaction matrices $A,B$ that encode the combined impact of Crowley–Martin saturation, regime switching, and jump noise. In terms of explicit inequalities involving ${\lambda }_k$ and the entries of $A,B$, we obtain sharp almost-sure criteria for extinction of all infectives, persistence with competitive exclusion, and coexistence in mean of both primary strains, together with the induced long-term behaviour of the co-infected class. Numerical simulations with regime switching and compensated Poisson jumps illustrate and support these thresholds. This provides, to our knowledge, the first rigorous extinction-exclusion-coexistence theory for a multi-strain SIS co-infection model under the joint influence of Crowley–Martin incidence, Markov switching, and Lévy perturbations. Full article

This paper studies optimal dividend and capital injection strategies with active exit options under a jump-diffusion model. We introduce a piecewise terminal payoff function to capture stop-loss exits (for deficits) and profit-taking exits (for surpluses), enabling shareholders to dynamically balance risk and return. Using the dynamic programming principle, we derive the associated quasi-variational inequalities (QVIs) and characterize the value function as the unique viscosity solution. To address analytical challenges, we employ the Markov chain approximation method, constructing a controlled Markov chain that closely approximates the jump-diffusion dynamics. Numerical solutions of the approximated problem are obtained via value iteration. The numerical results demonstrate how the value function and optimal strategies respond to different claim distributions (comparing Exponential and Pareto cases), key model parameters, and exit payoff functions. The numerical study further validates the algorithm’s convergence and examines the stability of solutions with respect to domain truncation in the QVI formulation. Full article

This paper develops a quantitative framework for climate–financial risk measurement that combines a spatially explicit jump–diffusion asset–loss model with prudentially aligned risk metrics. The approach connects regional physical hazards and transition variables derived from climate-consistent pathways to asset returns and credit parameters through the use of climate-adjusted volatilities and jump intensities. Fat tails and geographic heterogeneity are captured by it, which conventional diffusion-based or purely narrative stress tests fail to reflect. The framework delivers portfolio-level Spatial Climate Value-at-Risk (SCVaR) and Expected Shortfall (ES) across scenario–horizon matrices and incorporates an explicit robustness layer (block bootstrap confidence intervals, unconditional/conditional coverage backtests, and structural-stability tests). All ES measures are understood as Conditional Expected Shortfall (CES), i.e., tail expectations evaluated conditional on climate stress scenarios. Applications to bank loan books, pension portfolios, and sovereign exposures show how climate shocks reprice assets, alter default and recovery dynamics, and amplify tail losses in a region- and sector-dependent manner. The resulting, statistically validated outputs are designed to be decision-useful for Internal Capital Adequacy Assessment Process (ICAAP) and Pillar 2: climate-adjusted capital buffers, scenario-based stress calibration, and disclosure bridges that complement alignment metrics such as the Green Asset Ratio (GAR). Overall, the framework operationalises a move from exposure tallies to forward-looking, risk-sensitive, and auditable measures suitable for supervisory dialogue and internal risk appetite. Full article

We present a unified framework for modelling the term structure of interest rates using affine term structure models (ATSMs) with jumps and regime switches. The novelty lies in combining affine jump diffusion models with regime switching dynamics within a unified framework, allowing for state-dependent jump behaviour while preserving analytical tractability. This integration enables the model to simultaneously capture nonlinear market regimes and discontinuous movements in interest rates—features that traditional affine models or regime switching models alone cannot jointly represent. Estimation is carried out using the Unscented Kalman Filter (UKF) with the belief that it is capable of handling nonlinearity and therefore should estimate the non-Gaussian dynamics well. The yield curve fit demonstrates that both models fit our data well. RMSEs show that the regime switching affine jump diffusion (RS-AJD) model outperforms the affine jump diffusion (AJD) in-sample. Full article

Background/Objectives: The cerebellum contributes to both motor and cognitive functions. As basketball requires the integration of these abilities, basketball athletes provide an ideal model for exploring cerebellar adaptations. This study aimed to examine multidimensional cerebellar adaptations in basketball athletes and their associations with physical performance. Methods: In this study, 55 high-level basketball athletes and 55 non-athletes matched for age and gender were recruited for multimodal magnetic resonance imaging data collection and physical fitness tests. We compared the structural and functional differences in the brain between the two groups and analyzed the correlations between regional brain indices and physical fitness test outcomes. Results: Basketball athletes exhibited increased gray matter volume in Crus I, alongside heightened ALFF signal in Crus I and improved regional homogeneity in Crus II and VII b compared to non-athletes. Diffusion kurtosis imaging analysis demonstrated that athletes perform elevated kurtosis fractional anisotropy and decreased radial kurtosis within the cerebellar cortex and peduncles, with cortical modifications mainly localized around Crus I and lobule VI. Notably, both kurtosis fractional anisotropy and the amplitude of low-frequency fluctuations displayed positive correlations with vertical jump performance, an indicator specific to basketball ability. Conclusions: Basketball athletes exhibit structural, microstructural, and functional cerebellar adaptations, especially in Crus I. These modifications involve regions associated with motor and cognitive representations within the cerebellum, and part of the indexes are linked to the athletes’ physical performance. This study enhances our understanding of cerebellar adaptive changes in athletes, providing new insights for future research aimed at fully elucidating the role of the cerebellum in these individuals. Full article

This paper investigates a robust optimal reinsurance and investment problem for an insurance company operating in a Markov-modulated financial market. The insurer’s surplus process is modeled by a diffusion process with jumps, which is correlated with financial risky assets through a common shock structure. The economic regime switches according to a continuous-time Markov chain. To address model uncertainty concerning both diffusion and jump components, we formulate the problem within a robust optimal control framework. By applying the Girsanov theorem for semimartingales, we derive the dynamics of the wealth process under an equivalent martingale measure. We then establish the associated Hamilton–Jacobi–Bellman (HJB) equation, which constitutes a coupled system of nonlinear second-order integro-differential equations. An explicit form of the relative entropy penalty function is provided to quantify the cost of deviating from the reference model. The theoretical results furnish a foundation for numerical solutions using actor–critic reinforcement learning algorithms. Full article

Bayesian analysis is particularly useful for inferring models and their parameters given data. This is a common task in metabolic modeling, where models of varying complexity are used to interpret data. Nested sampling is a class of probabilistic inference algorithms that are particularly effective for estimating evidence and sampling the parameter posterior probability distributions. However, the practicality of nested sampling for metabolic network inference has yet to be studied. In this technical report, we explore the amalgamation of nested sampling, specifically diffusive nested sampling, with reversible jump Markov chain Monte Carlo. We apply the algorithm to two synthetic problems from the field of metabolic flux analysis. We present run times and share insights into hyperparameter choices, providing a useful point of reference for future applications of nested sampling to metabolic flux problems. Full article

Accurate modeling of event sequences is valuable in domains like electronic health records, financial risk management, and social networks. Random time intervals in these sequences contain key dynamic information, and temporal point processes (TPPs) are widely used to analyze event triggering mechanisms and probability evolution patterns in asynchronous sequences. Neural TPPs (NTPPs) enhanced by deep learning improve modeling capabilities, but most suffer from limited interpretability due to predefined functional structures. This study proposes KANJDP (Kolmogorov–Arnold Neural Jump-Diffusion Process), a novel event sequence modeling method: it decomposes the intensity function via stochastic differential equations (SDEs), with each component parameterized by learnable spline functions. By analyzing each component’s contribution to event occurrence, KANJDP quantitatively reveals core event generation mechanisms. Experiments on real-world and synthetic datasets show that KANJDP achieves higher prediction accuracy with fewer trainable parameters. Full article

Each charging/discharging cycle leads to a gradual decrease in the battery’s capacity. The degradation of capacity in lithium-ion batteries represents a non-monotonous process with random jumps. Earlier studies claimed that the instantaneous degradation value of a lithium-ion battery is influenced by the historical dataset with long-range dependence. The existing methods ignore large jumps and long-range dependences in degradation processes. In order to capture long-range-dependent behavior with random jumps, we refer to the fractional Poisson process. We also outline the relationship between the long-range correlation and the Hurst index. The connection between random jumps in capacitance and long-range dependence of the fractional Poisson process is proven. In order to construct the fractional Poisson predictive model, we included fractional Brownian motion as the diffusion term and the fractional Poisson process as the jump term. The proposed approach is implemented on NASA’s dataset for Li-ion battery degradation. We believe that the error analysis for the fractional Poisson process is advantageous compared with that of the fractional Brownian motion, the fractional Levy stable motion, the Wiener model, and the long short-term memory model. Full article

The digital creative industries have emerged as a critical driver of regional economic transformation, upgrading, and sustainable development. While previous research has primarily focused on creative industry layout and agglomeration in urban areas, with the integration of digital technology and the creative industry, existing research has an insufficient explanation for the digital creative industry. Specifically, few people have studied the spatial distribution and diffusion of digital creative industries in emerging economies from the macro-regional level. To address this gap, this study analyzes the spatial diffusion mode and regional spatial response law of digital creative industries in the Yangtze River Delta during three critical time windows (2016, 2019, and 2022) in the context of national strategy implementation. A range of spatial analysis technologies is utilized to process the full sample of big data from digital creative industries. This study utilizes OLS and a quantile regression model to determine the dominant factors that affect spatial diffusion and response in the digital creative industries. The results demonstrate that, against the backdrop of regional development strategies, digital creative industries exhibit a variety of diffusion modes, including contagious, hierarchical, corridor, and jump diffusion. The response of industries to regional strategies has different rules in terms of regional space, urban development, and sub-industries. Furthermore, the comprehensive influence of institutional environment, urban economy, development and innovation significantly impacts industrial spatial diffusion and regional response. Among them, government investment in science and technology and the number of universities have consistently been important influencing factors, and policy exhibits nonlinear effects and asymmetric characteristics on industry agglomeration and diffusion. This study enhances the understanding of digital creative industry development in the YRD and offers a theoretical basis for optimizing regional industrial spatial structure and promoting the sustainable development of digital industries. Full article

The numerical simulation of unsteady, high-Reynolds-number incompressible flows governed by the Navier–Stokes (NS) equations presents significant challenges in computational fluid dynamics, primarily concerning numerical stability and computational efficiency. Standard Galerkin finite element methods often suffer from non-physical oscillations in convection-dominated regimes, while the multiscale nature of these flows demands prohibitively high computational resources for uniformly refined meshes. This paper proposes an improved Galerkin framework that synergistically integrates a Variational Multiscale Stabilization (VMS) method with an adaptive mesh refinement (AMR) strategy to overcome these dual challenges. Based on the Ritz–Galerkin formulation with the stable Taylor–Hood ($P_2-P_1$) element, a VMS term is introduced, derived from a generalized $\theta$-scheme. This explicitly constructs a subgrid-scale model to effectively suppress numerical oscillations without introducing excessive artificial diffusion. To enhance computational efficiency, a novel a posteriori error estimator is developed based on dual residuals. This estimator provides the robust and accurate localization of numerical errors by dynamically weighting the momentum and continuity residuals within each element, as well as the flux jumps across element boundaries. This error indicator guides an AMR algorithm that combines longest-edge bisection with local Delaunay re-triangulation, ensuring optimal mesh adaptation to complex flow features such as boundary layers and vortices. Furthermore, the stability of the Taylor–Hood element, essential for stable velocity–pressure coupling, is preserved within this integrated framework. Numerical experiments are presented to verify the effectiveness of the proposed method, demonstrating its ability to achieve stable, high-fidelity solutions on adaptively refined grids with a substantial reduction in computational cost. Full article

With the deepening of degradation, the stability and reliability of the degrading system usually becomes poor, which may lead to random jumps occurring in the degradation path. A non-homogeneous jump diffusion process model is introduced to more accurately capture this type of degradation. In this paper, the proposed degradation model is translated into a state–space model, and then the Monte Carlo simulation of the state dynamic model based on particle filtering is employed for predicting the degradation evolution and estimating the remaining useful life (RUL). In addition, a general model identification approach is presented based on maximization likelihood estimation (MLE), and an iterative model identification approach is provided based on the expectation maximization (EM) algorithm. Finally, the practical value and effectiveness of the proposed method are validated using real-world degradation data from temperature sensors on a blast furnace wall. The results demonstrate that our approach provides a more accurate and robust RUL estimation compared to CNN and LSTM methods, offering a significant contribution to enhancing predictive maintenance strategies and operational safety for systems with complex, non-monotonic degradation patterns. Full article

This study investigates the valuation of Euro-convertible bonds (ECBs) using a novel Markov-modulated cojump-diffusion (MMCJD) model, which effectively captures the dynamics of stochastic volatility and simultaneous jumps (cojumps) in both the underlying stock prices and foreign exchange (FX) rates. Furthermore, we introduce a Markov-modulated Cox–Ingersoll–Ross (MMCIR) framework to accurately model domestic and foreign instantaneous interest rates within a regime-switching environment. To manage computational complexity, the least-squares Monte Carlo (LSMC) approach is employed for estimating ECB values. Numerical analyses demonstrate that explicitly incorporating stochastic volatilities and cojumps significantly enhances the realism of ECB pricing, underscoring the novelty and contribution of our integrated modeling approach. Full article

Modeling of impurity diffusion processes in a multiphase randomly inhomogeneous body is performed using the Feynman diagram technique. The impurity diffusion equations are formulated for each of the phases separately. Their random boundaries are subject to non-ideal contact conditions for concentration. The contact mass transfer problem is reduced to a partial differential equation describing diffusion in the body as a whole, which accounts for jump discontinuities in the searched function as well as in its derivative at the stochastic interfaces. The obtained problem is transformed into an integro-differential equation involving a random kernel, whose solution is constructed as a Neumann series. Averaging over the ensemble of phase configurations is performed. The Feynman diagram technique is developed to investigate the processes described by parabolic partial differential equations. The mass operator kernel is constructed as a sum of strongly connected diagrams. An integro-differential Dyson equation is obtained for the concentration field. In the Bourret approximation, the Dyson equation is specified for a multiphase randomly inhomogeneous medium with uniform phase distribution. The problem solution, obtained using Feynman diagrams, is compared with the solutions of diffusion problems for a homogeneous layer, one having the coefficients of the base phase and the other having the characteristics averaged over the body volume. Full article