Efficient numerical method for time-fractional Black-Scholes model.
problem Solving time-fractional Black-Scholes equations for European options.
method Crank-Nicolson discretization for time, exponential B-spline for space.
result The proposed method is unconditionally stable and superior to existing approaches.
New method combines ODE filters and numerical quadrature to propagate model uncertainty.
problem Propagation of model uncertainty in ODE solutions with uncertain parameters.
method Combining ODE filters with numerical quadrature.
result Effective propagation of both numerical and parametric uncertainty.
Study shows how numerical discretization affects reconstructions and parameter distributions in nano metrology.
problem Impact of numerical discretization on parameter reconstructions and model parameter distributions.
method Bayesian target vector optimization, finite element model, Gaussian process, stochastic machine learning surrogate models, Markov chain Monte Carlo sampler.
result Numerical discretization parameters impact the accuracy and distribution of reconstructed model parameters.
Introduces numerical Gaussian process Kalman filtering for infinite-dimensional systems.
problem Kalman filtering on infinite-dimensional systems.
method Embedding numerical Gaussian processes into Kalman filter equations.
result Ability to perform Kalman filtering on infinite-dimensional systems using Gaussian processes.
Language models can predict numeric values as strings.
problem Regression tasks with numeric predictions.
method Causal sequence decoding models trained for next-token prediction.
result Decoder-based heads perform as well as standard heads in numeric regression tasks.
The paper solves complex swing option pricing equations with numerical methods.
problem Valuation of swing options with jumps under a mean-reverting model.
method Proposes second-order numerical methods to solve PIDEs convection-dominated and with nonlocal integral terms.
result Numerical methods confirm second-order convergence behavior.
Paper introduces NumLLM for better financial text understanding with numeric variables.
problem Poor performance of existing financial large language models in numeric financial text.
method Constructed financial corpus, fine-tuned with LoRA modules, merged into foundation model.
result NumLLM achieves best performance on financial question-answering benchmark, especially with numeric questions.
Develops a numerical method for LRM strategies in BNS models with infinite active jumps.
problem Calculating locally risk-minimizing strategies for non-martingale BNS models with infinite active jumps.
method Modified Malliavin calculus expression and Monte Carlo method for non-martingale BNS models.
result Proposes a numerical method for LRM strategies in non-martingale BNS models with infinite active jumps.
FiNCAT tool automatically identifies financial numerals in documents.
problem Differentiating between in-claim and out-of-claim numerals in financial documents.
method Extracts context embeddings of numerals using BERT, then uses Logistic Regression to classify.
result Achieved a Macro F1 score of 0.8223 on validation set.
The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.
problem Numerical integration challenges in SV models, especially with high precision and low computational time.
method Proposes a fast regime switching algorithm to determine when higher precision arithmetic is needed.
result Shows that numerical quadratures need to be carefully chosen based on model parameters and parameter values.
LLMs struggle with arithmetic tasks unless they use high numerical precision.
problem Improving arithmetical reasoning capabilities of LLMs.
method Theoretical analysis and empirical experiments on numerical precision.
result LLMs require high numerical precision to efficiently handle arithmetic tasks.
Recognizing written domain numeric utterances (e.g. I need $1.25.) can be challenging for ASR systems, particularly when numeric sequences are not seen during training. This out-of-vocabulary (OOV) issue is addressed in conventional ASR systems by training part of the model on spoken domain utterances (e.g. I need one …
Study validates Libor model for insurance benefits calculation.
problem Valuation of long-term insurance guarantees.
method Mean-field Libor market model, numerical ALM, aggregated life insurance data.
result Derives estimators for future discretionary benefits.
This paper tackles Bayesian system identification with probabilistic numerical methods.
problem Accurately modeling nonlinear dynamic systems from noisy data.
method Probabilistic Sequential Monte Carlo (SMC) combined with probabilistic numerical integration.
result Efficient identification of latent states and system parameters from noisy measurements.
Probabilistic numerics expands numerical tasks with black box methods.
problem Difficult conditioning of random variables in numerical tasks.
method Construct probabilistic numerical methods based on final outputs, extrapolating limiting quantities.
result Higher orders of convergence achieved in various numerical tasks.
New model combines physics and machine learning for ocean dynamics.
problem Discovering hidden laws governing ocean dynamics.
method Develops Deep Neural Numerical Models (DNNMs) to learn hidden variables of physical laws.
result Illustrates DNNMs applied to Sea Surface Height dynamics, connecting to QG model.
Calibration of stochastic local volatility (SLV) models to their underlying local volatility model is often performed by numerically solving a two-dimensional non-linear forward Kolmogorov equation. We propose a novel finite volume (FV) discretization in the numerical solution of general 1D and 2D forward Kolmogorov eq…
We first estimate the average growth of a company's annual income and its variance by using both real company data and a numerical model which we already introduced a couple of years ago. Investment strategies expecting for income growth is evaluated based on the numerical model. Our numerical simulation suggests the p…
Derives a rough SABR formula for short maturities.
problem Modeling volatility smiles under rough volatility.
method Derives an ODE and solves it numerically.
result Develops a very accurate approximation called the rough SABR formula.
Develops numerical methods for pricing exchange options in a market with limited liquidity.
problem Pricing European style exchange options in a market with finite liquidity.
method Integrates price impact into the dynamics of correlated assets using a controlled variate approach.
result Numerical pricing methods for exchange options are developed and validated.
We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical study we obtain high-order numerical convergence also for non-zero …
Space mapping speeds up shape optimization for PDEs.
problem Efficiently solving shape optimization problems constrained by PDEs.
method Combines fine and coarse model optimizations using Riemannian metrics.
result Space mapping methods are highly efficient for complex shape optimization problems.
By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the…
This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock's price. Thus, we consider a full-feedback model in which price impact is fully incorporated into the model. The price …
We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite dimensional system of stochastic dif…
xVal tokenizes numbers continuously for better scientific model training.
problem Lack of continuous numerical tokenization for scientific datasets in LLMs.
method xVal: Continuous numerical tokenization strategy.
result xVal outperforms other numerical tokenization methods on scientific datasets.
In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distrib…
Numeracy is the ability to understand and work with numbers. It is a necessary skill for composing and understanding documents in clinical, scientific, and other technical domains. In this paper, we explore different strategies for modelling numerals with language models, such as memorisation and digit-by-digit composi…
A novel graph spectral method for mixed categorical and numerical data.
problem Feature learning for mixed data types (numerical and categorical).
method Graph spectral decomposition of the graph Laplacian to model probabilistic dependence structure.
result Increased separability and clusterability of observations in the transformed feature space.
Bayesian Topic Regression models causal inference with text and numerical data.
problem Causal inference using observational text data with both text and numerical confounders.
method Combines supervised Bayesian topic model with Bayesian regression framework, respecting the Frisch-Waugh-Lovell theorem.
result Joint approach recovers ground truth with lower bias than benchmarks, superior prediction results compared to separate approaches.
Despite the importance of handwritten numeral classification, a robust and effective method for a widely used language like Arabic is still due. This study focuses to overcome two major limitations of existing works: data diversity and effective learning method. Hence, the existing Arabic numeral datasets have been mer…
In this Article, a fast numerical numerical algorithm for pricing discrete double barrier option is presented. According to Black-Scholes model, the price of option in each monitoring date can be evaluated by a recursive formula upon the heat equation solution. These recursive solutions are approximated by using Legend…
Method detects errors in numerical data using regression models.
problem Noise and errors in numerical datasets.
method Introduced veracity scores and a filtering procedure for error detection.
result Method outperforms other approaches in identifying incorrect values.
Model uses LLMs to process numerical data guided by natural language descriptions.
problem Challenges in integrating prior knowledge into probabilistic models.
method Developed LLM Processes to condition numerical predictive distributions on natural language.
result Improved predictive performance and structured qualitative descriptions.
We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we work out weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to deal with the …
New formula for efficient spread option pricing in copula markets.
problem Efficient pricing of spread options in markets with correlated assets.
method Unified approach using copula functions and numerical integration.
result Proposes a method requiring only one-dimensional integral evaluations.
Efficient method for lookback option pricing under Markov models.
problem Pricing lookback options under Markov models.
method Model-free representations combined with numerical quadrature and Markov chain approximation.
result Efficient method applicable to various Markov models.
This paper compares analytical and numerical solutions of the Black-Scholes model.
problem Comparing analytical and numerical methods for solving the Black-Scholes model.
method Analytical solution (variable separation) and numerical solution (finite differences) of the Black-Scholes equation.
result Numerical solutions provide more accurate results for complex scenarios.
The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal inverse Gaussian process, using the results of Arai et al. \cite{AIS}, and Arai …
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly dete…
Neural ODEs' performance varies with numerical method, requiring adaptive step size control.
problem Neural ODEs' performance depends on the numerical method used during training.
method Proposes an adaptive step size control algorithm to ensure a valid ODE without increasing computational cost.
result Valid Neural ODEs require careful numerical method selection and step size adaptation.
PNDMs accelerate DDPMs by treating them as differential equations on manifolds.
problem Accelerate DDPMs while maintaining sample quality.
method Propose pseudo numerical methods (PNDMs) to solve differential equations on manifolds.
result PNDMs generate higher quality images with only 50 steps compared to 1000-step DDIMs (20x speedup).
Conditions of Stability for explicit finite difference scheme and some results of numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon are provided. It seems to be difficult to get solution formula for PDE model which generalizes Agliardi's …
New findings on optimal transport gradient for generative models, addressing numerical instabilities.
problem Numerical instabilities in training Wasserstein Generative Adversarial Networks (WGAN).
method Valid differentiation theorem for entropic regularized transport, semi-discrete gradient formulation, and optimization algorithm.
result Existence of optimal transport gradient for generative models under specified conditions.
End-to-end solution for recognizing handwritten numerals, avoiding traditional preprocessing steps.
problem Handwritten numeral string recognition with traditional preprocessing steps.
method YoLo-based model for automatic detection and recognition, avoiding heuristic-based preprocessing and segmentation.
result Proposed method reduces complexity and is a feasible end-to-end solution for numeral string recognition.
New method models dewetting of anisotropic particles using numerical techniques.
problem Modeling dewetting dynamics of particles with varying surface energies.
method Level set numerical approach with convolution kernels to handle anisotropic interfacial energies.
result Validated numerical scheme supports merging and splitting of interfaces.
Study uses neural networks to solve complex equations efficiently.
problem Solving parametric partial differential equations.
method Machine learning and deep neural networks.
result Performance of the model is independent of parameter space dimension.
Study proposes Local Linear Encoding for better feature discretization.
problem Improving feature discretization for numeric data.
method Theoretical analysis and Local Linear Encoding (LLE) method.
result LLE outperforms conventional methods with fewer parameters.