Extends saddle-point method for large-time volatility smiles.
problem Analyzing large-time volatility smiles in financial models.
method Saddle-point approach to derive large-time model-implied volatility smiles.
result Provides theoretical foundation and wide class of arbitrage-free parametrizations.
Paper develops large time series models using pre-trained transformers.
problem Performance bottlenecks in small models on data-scarce scenarios.
method Large-scale pre-training, unified time series format, GPT-style architecture.
result Generative pre-trained Time Series Transformer (Timer) for diverse tasks.
A faster method for visualization recommendations on large datasets.
problem Infeasibility of state-of-the-art vis-rec models on large datasets due to high computational time.
method Reinforcement-learning (RL) framework that identifies optimal statistics within a time budget.
result Significantly reduces time-to-visualize with minimal error compared to baseline approaches.
We investigate the large-volatility dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after large volatilities is characterized by a power law, and the exponents p± usually vary with the strength of the large vo…
ISALT uses inference to simulate SDEs with large time-steps, improving efficiency.
problem Efficiently simulating ergodic SDEs with large time-steps.
method Inference-based schemes adaptive to large time-steps (ISALT) from data.
result ISALT achieves significant time reduction and optimal accuracy.
Shorter proof for wave front length in Euclidean disk
problem Wave front length in Euclidean disk
method Shorter proof and computation of oscillating corrections
result Linear asymptotics of wave front length in large time
We investigate the large-fluctuation dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after the large fluctuations is characterized by a power law, and the exponents p± usually vary with the strength of the lar…
Deep learning accelerates Monte Carlo SDE simulations with large time steps.
problem Accurate simulation of SDEs with large time steps.
method Polynomial chaos expansion with neural network learned stochastic collocation points.
result Data-driven scheme achieves strong convergence in Monte Carlo simulations.
Study volatility models with rough paths, focusing on large deviations and option behavior.
problem Analyzing volatility in financial markets with very rough paths.
method Introduced time-inhomogeneous stochastic volatility models with Volterra Gaussian processes.
result Obtained large deviation principles for log-price processes in super rough Gaussian models.
This work aims to create a large-scale model for critical care time series data.
problem Lack of large-scale datasets and distribution shifts in critical care time series data.
method Harmonized dataset creation and transfer learning research.
result Established a foundation for large-scale multi-variate time series models in critical care.
We derive large time upper bounds for heat kernels on vector bundles of differential forms on a class of non-compact Riemannian manifolds under certain curvature conditions.
The paper studies heat kernel behavior on symmetric spaces.
problem Large-time behavior of heat operator traces on symmetric spaces.
method Uses representation theory and Carmona's proof of Vogan's lambda map.
result Provides an asymptotic formula for heat kernel behavior.
Paper introduces a new method to compute pseudoinverse for ELM with large datasets.
problem Efficient computation of pseudoinverse for ELM with large datasets.
method Rank-based matrix decomposition of the hidden layer matrix.
result Optimal training time and reduced computational complexity for large hidden nodes.
For any closed Riemannian manifold X we prove that large isoperimetric regions in X×Rn are of the form X×(Euclidean ball). We prove that if X has non-negative Ricci curvature then the only soap bubbles enclosing a large volume are the products X×(Euclidean sphere). We give an example…
Scalable hybrid HMM with Gaussian Process for time-series data clustering.
problem Large number of parameters and long sequences in time-series data make HMM-GPSM training difficult.
method Stochastic Variational Inference (SVI) for long sequences and reparameterized random Fourier features (R-RFF) for large data points.
result Significant reduction in training time and improved hidden-state estimation accuracy.
This paper derives explicit formulas for both the small and large time limits of the implied volatility in the minimal market model. It is shown that interest rates do impact on the implied volatility in the long run even though they are negligible in the short time limit.
We propose a novel time discretization for the log-normal SABR model and derive its asymptotic properties.
problem Analyzing the log-normal SABR model's time-discretized behavior and implied volatility surface.
method We use the Euler-Maruyama scheme for time discretization and derive asymptotic properties in the limit of large number of time steps.
result We derive an exact representation of the implied volatility surface for arbitrary maturity and strike in the asymptotic regime.
Optimizes variance reduction in Heston model using large and moderate deviations.
problem Improving variance reduction in stochastic volatility models.
method Large and moderate deviations theory applied to Heston model.
result Derives closed-form solutions for optimal change of measure.
Fine-tuning a time series model improves financial price prediction accuracy.
problem Improving accuracy in predicting financial market prices using large models.
method Continual pre-training of a time series foundation model on financial data to fine-tune its performance for price prediction.
result The fine-tuned model outperforms the baseline in various financial metrics.
Given a compact Riemannian manifold M without boundary, we show that large isoperimetric regions in M×Rk are tubular neighborhoods of M×{x}, with x∈Rk.
We study here the large-time behaviour of all continuous affine stochastic volatility models (in the sense of Keller-Ressel) and deduce a closed-form formula for the large-maturity implied volatility smile. Based on refinements of the Gartner-Ellis theorem on the real line, our proof reveals pathological behaviours of …
BayTiDe discovers time-delayed differential equations from noisy data.
problem Discovering time-delayed differential equations from data with large delays and noise.
method Bayesian inference with a sparsity-promoting prior.
result BayTiDe accurately identifies time-delayed differential equations with accuracy proportional to data resolution.
New method recovers causal networks from short time-series data.
problem Inferring causal relationships from short time-series data in complex systems.
method Large-scale Nonlinear Granger Causality (lsNGC) approach.
result Captures meaningful interactions from limited observational data.
Large deviation principles for multivariate stochastic volatility models.
problem Understanding the behavior of log-processes in multivariate stochastic volatility models.
method Establishing a comprehensive sample path large deviation principle for log-processes.
result Asymptotic formulas for first exit times and barrier option prices derived from the LDP.
We propose to solve large scale Markowitz mean-variance (MV) portfolio allocation problem using reinforcement learning (RL). By adopting the recently developed continuous-time exploratory control framework, we formulate the exploratory MV problem in high dimensions. We further show the optimality of a multivariate Gaus…
New method speeds up Gaussian process training and inference for large datasets.
problem Training and inference in Gaussian processes are computationally expensive for large datasets.
method Iterative alternating projection method that accesses subblocks of the kernel matrix, reducing time and space complexity.
result Empirically, the method accelerates GP training and inference by up to 72x compared to conjugate gradients.
We consider the porous medium equation with power-type reaction terms up on negatively curved Riemannian manifolds, and solutions corresponding to bounded, nonnegative and compactly supported data. If p>m, small data give rise to global-in-time solutions while solutions associated to large data blow up in finite t…
We study the small-time behaviour of the rough Bergomi model, introduced by Bayer, Friz and Gatheral (2016), and prove a large deviations principle for a rescaled version of the normalised log stock price process, which then allows us to characterise the small-time behaviour of the implied volatility.
Deep learning speeds spectral density estimation for large 2D/3D grids.
problem Computational challenges in estimating spectral densities for large grids.
method Deep learning neural network for spectral density estimation.
result Deep learning estimator is a universal approximator and faster than existing methods.
GPU speeds up Monte Carlo simulations for large time steps.
problem Slow convergence and inaccurate solutions with large time steps in Monte Carlo simulations.
method Generalizes the Seven League scheme for GPU acceleration.
result Significantly improved computational speed.
A new algorithm speeds up CP decomposition for large tensors.
problem Efficiently processing large-scale tensors in real-time.
method Randomized online CP decomposition (ROCP) algorithm.
result ROCP reduces computing time and memory usage significantly.
New framework uses time series features for predicting streamflow in ungauged areas.
problem Predicting streamflow in areas without gauging stations.
method Developed regression-based streamflow regionalization using a wide range of time series features from large datasets.
result Certain time series features, like entropy and autocorrelation, are better predictors of streamflow than traditional catchment attributes.
We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and tail asymptotics for diffusions, as well as for option prices and realised vari…
Study shows how large neural networks avoid overfitting through decoupling of feature learning and complexity growth.
problem Understanding inductive bias and generalization in large neural networks.
method Dynamical mean field theory applied to large two-layer networks.
result Training dynamics of large networks exhibit a separation of timescales, decoupling feature learning and overfitting.
The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps.…
TSFMs improve financial forecasting from diverse datasets.
problem Challenges in forecasting financial time series due to noisy, non-stationary, and heterogeneous data.
method Empirical study of TSFMs in global financial markets, evaluating zero-shot inference, fine-tuning, and pre-training from scratch.
result Pre-trained TSFMs on financial data achieve substantial forecasting and economic improvements, highlighting the value of domain-specific adaptation.
The paper proves the regularity of cohomogeneity two problems and constructs minimal hypersurfaces on spheres.
problem Cohomogeneity two equivariant isotopy minimization problems and minimal hypersurfaces with large Betti numbers.
method Developed cohomogeneity two equivariant min-max theory for minimal hypersurfaces.
result Constructs minimal hypersurfaces on spheres with large Betti numbers and specific symmetries.
The probability minimizing problem of large losses of portfolio in discrete and continuous time models is studied. This gives a generalization of quantile hedging presented in [3].
Sparse Markovian Gaussian processes improve probabilistic model inference for large datasets.
problem Efficient inference for large-scale time series data.
method Combining inducing variables with Kalman filter-like recursions for linear scaling.
result General site-based approach for approximating non-Gaussian likelihoods.
Optimal model selection for forecasting large collections of short time series using latent space.
problem Challenges in choosing among multiple forecasting methods for large, high-dimensional time series with limited data.
method Combining low-rank temporal matrix factorization with optimal model selection using cross-validation.
result Forecasting latent factors leads to significant performance gains compared to direct uni-variate model application.
The study examines how extra compute during testing affects the performance of large language models.
problem Understanding the conditions under which test-time scaling improves model performance.
method An in-context weight prediction task for linear regression was used to train transformers. The performance was analyzed under varying levels of test-time compute.
result Training transformers on diverse, relevant, and hard tasks leads to the best performance for test-time scaling.
Efficient algorithms improve learning of large-margin halfspaces.
problem Learning large-margin halfspaces efficiently and reproducibly.
method Design of efficient, dimension-independent, polynomial-time algorithms; SGD-based approach; DP-to-Replicability reduction.
result Improved sample complexity compared to previous algorithms, with optimal sample complexity for one algorithm.
For a broad range of research, governmental and commercial applications it is important to understand the allegiances, communities and structure of key players in society. One promising direction towards extracting this information is to exploit the rich relational data in digital social networks (the social graph). As…
TaLK Convolutions improve sequence modeling efficiency.
problem Efficiently modeling sequences with limited time complexity.
method Adaptive convolution operation that learns kernel size.
result Time complexity reduced to O(n), making sequence encoding linear. Game theory model shows optimal investment strategy for wealth growth.
problem Minimizing time to reach large wealth in a stochastic asset market.
method Proved strategy of proportional asset investment minimizes expected time.
result Proportional investment strategy asymptotically minimizes time to large wealth.
We consider the dynamics of player's strategies in repeated market games, where the selection of strategies is determined by a learning model. Prior theoretical analysis and experimental data show that after large number of plays the average number of agents who decide to enter, per round of the game, approaches the ma…
SWAP uses large mini-batches to train DNNs faster with good generalization.
problem Training deep neural networks with small mini-batches is time-consuming.
method SWAP computes an approximate solution with large mini-batches and refines it by averaging weights of multiple parallel models.
result SWAP trains models as well as small-batch training but in significantly less time.
We build a simple diagnostic criterion for approximate factor structure in large cross-sectional equity datasets. Given a model for asset returns with observable factors, the criterion checks whether the error terms are weakly cross-sectionally correlated or share at least one unobservable common factor. It only requir…