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.
Study efficient numerical methods for American basket options.
problem Valuation of American basket options.
method Partial differential complementarity problems (PDCPs) and efficient discretization.
result Approximations of American basket options are close and converge favourably.
FBSJNN solves PIDEs and FBSDEJs with deep learning, offering theoretical and numerical efficiency.
problem Solving Partial Integro-Differential Equations and Forward-Backward Stochastic Differential Equations with Jumps.
method FBSJNN framework using a single neural network for both solution approximation and non-local integral.
result FBSJNN achieves numerical solutions with a relative error of 10−3, demonstrating efficiency. 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.
SINGD improves KFAC for memory-efficiency and stability in low-precision training.
problem Memory inefficiency and numerical instability of KFAC in low-precision training.
method Formulated inverse-free KFAC update and imposed structures in Kronecker factors.
result SINGD is memory-efficient and numerically robust, often outperforming AdamW in half precision.
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.
Improved MLMC method for robust and efficient probability and density estimation.
problem Stability and poor complexity of MLMC for low-regularity functionals.
method Numerical smoothing combined with MLMC for deterministic quadrature methods.
result Significant improvement in strong convergence and robustness of MLMC method.
New ODE solvers improve training efficiency and accuracy.
problem Training Neural ODEs requires efficient and accurate gradient calculation.
method Presented algebraically reversible ODE solvers that are time and memory efficient, calculate exact gradients, and are numerically stable.
result Reversible solvers strictly improve upon previous architectures in efficiency and accuracy.
NCG methods improve shape optimization efficiency.
problem Shape optimization problems
method Nonlinear conjugate gradient methods
result NCG methods are efficient for shape optimization
Deep learning solves high-dimensional PDEs efficiently.
problem Solving high-dimensional Kolmogorov PDEs numerically.
method Reformulating as a statistical learning problem using Feynman-Kac formula.
result Single neural network learns entire family of PDEs.
CoLA automates efficient numerical linear algebra for complex matrix structures.
problem Efficiently solving large-scale linear algebra problems with complex matrix structures.
method Combining linear operator abstraction with compositional dispatch rules.
result Automatic and efficient numerical algorithms for various linear algebra operations.
The paper evaluates functions of stable Lévy processes and their extrema efficiently.
problem Efficiently evaluating functions of stable Lévy processes and their extrema.
method Integral representations, conformal acceleration technique, simplified trapezoid rule.
result Efficient numerical procedures for cumulative probability distribution functions (cpdfs) are developed.
New method uses tensor trains for efficient PDE approximation.
problem High-dimensional PDEs and the curse of dimensionality.
method Tensor trains and backward stochastic differential equations for parabolic PDEs.
result Achieves a favorable trade-off between accuracy and computational efficiency.
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.
In this paper, we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in details and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff-Schwartz…
Efficiently approximates integrals using a subset of samples from a target distribution in RKHS.
problem Approximating integrals with a target distribution using limited pointwise evaluations.
method Proposes a procedure using a small random subset of samples from the target distribution, either uniformly or using approximate leverage scores.
result Upper bound on approximation error for both sampling strategies, achieving optimal rate with reduced evaluations.
Efficient method for vertex embedding and community detection.
problem Vertex embedding and community detection.
method Normalized one-hot graph encoder and rank-based cluster size measure.
result Excellent numerical performance of graph encoder ensemble algorithm.
The paper derives formulas for option pricing and random walk expectations.
problem Calculating the price of barrier and lookback options.
method Inverse Z-transform, Fourier/Laplace inversion, Wiener-Hopf factorization, and numerical methods.
result Efficient numerical methods for option pricing are developed.
The original Broad Learning System (BLS) on new added nodes and its existing efficient implementation both assume the ridge parameter lambda -> 0 in the ridge inverse to approximate the generalized inverse, and compute the generalized inverse solution for the output weights. In this paper, we propose two ridge solution…
Improved method for numerical conformal mappings on complex domains.
problem Accurate and efficient computation of conformal mappings on multiply connected domains.
method Generalization and refinement of the conjugate function method using high-order finite element methods.
result Achieved accurate and efficient construction of boundary values for multiply connected domains.
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to incomplete/finite information about the continuous mathematical problem being approxi…
New method smooths integrands for efficient option pricing.
problem Improving numerical performance of option pricing methods.
method Combining hierarchical adaptive sparse grids, quasi-Monte Carlo, and numerical smoothing.
result Improved efficiency of ASGQ and QMC methods for high-dimensional problems.
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.
DNA-SE uses deep learning to solve semiparametric problems efficiently.
problem Solving semiparametric integral equations in high dimensions.
method Formulates semiparametric estimation as a bi-level optimization problem and uses DNN to approximate solutions.
result Demonstrates numerical and statistical advantages over traditional methods.
The ability to decompose a signal in an orthonormal basis (a set of orthogonal components, each normalized to have unit length) using a fast numerical procedure rests at the heart of many signal processing methods and applications. The classic examples are the Fourier and wavelet transforms that enjoy numerically effic…
The paper efficiently solves a complex option valuation equation for two assets.
problem Valuation of European options under a two-asset Kou jump-diffusion model.
method Extends an efficient algorithm for a one-dimensional integral to a two-dimensional one, using operator splitting schemes for time discretization.
result The method achieves optimal computational cost and stable convergence for various operator splitting schemes.
Efficiently approximates eigenspaces for symmetric and general matrices.
problem Fast computation of eigenspaces for large matrices.
method Factor eigenspaces into fundamental components using transformations, solve minimization problems, and iteratively update.
result Improved computational efficiency for eigenspace approximation.
We consider the numerical approximation of the quantile hedging price in a non-linear market. In a Markovian framework, we propose a numerical method based on a Piecewise Constant Policy Timestepping (PCPT) scheme coupled with a monotone finite difference approximation. We prove the convergence of our algorithm combini…
Develops efficient methods for approximating densities of financial models with jumps.
problem Approximating densities of affine jump diffusions with state-independent jump intensities.
method Recursive approach for deriving closed-form solutions to moments, constructing density approximations via moment matching.
result Superior computational efficiency and precision in option pricing and simulation compared to existing techniques.
Novel numerical scheme for G-heat equation with uncertainty.
problem Efficiently quantify G-expectation for financial products.
method Proposes a novel numerical scheme for the two-dimensional G-heat equation.
result The scheme is monotonic, stable, and convergent, showing high efficiency.
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme and its analysis of genera…
New approach improves computational efficiency of Bass Local Volatility model.
problem Eliminate interpolation and improve computational efficiency in local volatility models.
method Combines local quadratic estimation and lognormal mixture tails for state price densities; uses trapezoidal rule for numerical convolutions.
result Proposed method outperforms traditional numerical methods in option pricing and market case studies.
We propose an efficient lattice procedure which permits to obtain European and American option prices under the Black and Scholes model for digital options with barrier features. Numerical results show the accuracy of the proposed method.
We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical i…
New method for pricing American options in time-dependent models, improving accuracy and efficiency.
problem Pricing American options in time-dependent models with improved accuracy and efficiency.
method Semi-analytical pricing using a nonlinear Volterra integral equation and numerical methods.
result Improved accuracy and efficiency in pricing American options compared to forward finite difference solvers.
Deep learning upscales geologic models efficiently.
problem Upscaling large-scale geologic models for efficient simulation.
method Theory-guided convolutional neural network (TgCNN) trained to approximate hydraulic conductivity relationships.
result Deep learning method achieves equivalent upscaling accuracy to numerical methods but with significantly improved efficiency.
Efficiently solves high-dimensional ODEs with probabilistic methods.
problem Solving high-dimensional ODEs with uncertainty quantification.
method Probabilistic numerical algorithm based on independence assumptions or Kronecker structure.
result Efficient probabilistic solutions for ODEs with millions of dimensions.
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…
A new method solves large-scale sparse group square-root Lasso problems efficiently.
problem Large-scale linearly constrained sparse group square-root Lasso problems.
method Dual semismooth Newton based augmented Lagrangian method (ALM).
result The proposed method efficiently solves the problem with numerical experiments demonstrating its effectiveness.
New algorithm extends Greville's method for partitioned matrices efficiently and stably.
problem Efficiently compute pseudoinverse of partitioned matrices without retraining.
method Incorporates inverse Cholesky factorization to reduce computational complexity and improve stability.
result 1 iteration to compute pseudoinverse of whole matrix from first part, addressing all cases.
We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants. A closed form formula relying on multivariate Gaussian cumulative distribution functions is established for a generalized version of the mul…
With ever-increasing computational demand for deep learning, it is critical to investigate the implications of the numeric representation and precision of DNN model weights and activations on computational efficiency. In this work, we explore unconventional narrow-precision floating-point representations as it relates …
Efficiently calculates Brazilian stock options with discrete dividends.
problem Accurately pricing Brazilian listed equity options with discrete dividends.
method Uses the fast Laplace transform for high-accuracy computation.
result Efficiently computes option premiums and Greeks with high accuracy.
In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thomée (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally parallelizable. It is shown that the method is very efficient for calculating vari…
Bayesian quadrature improves integration efficiency with invariant priors.
problem Efficient numerical integration with known structure.
method Invariance priors for bijective transformations in input domain.
result Superior performance in synthetic and real-world applications.
Paper proposes efficient method to calculate Fisher-Bingham distribution normalizing constant.
problem Efficiently calculating the normalizing constant of Fisher-Bingham distributions.
method Numerical integration with continuous Euler transform to Fourier-type integral representation.
result The method is fast and accurate, applicable to high-dimensional distributions.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
New estimator handles covariate shift with closed-form solution and super-efficiency.
problem Handling covariate shift in missing data and causal inference problems.
method Minimum Wasserstein distance estimation framework.
result Closed-form expression and super-efficiency relative to semiparametric efficient estimator.