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.
In this paper we prove a new inversion theorem and a refinement of an old support theorem for two Radon transforms on a symmetric space. Included are some new identities for the Abel transform and some results about the Fourier transform from a joint work with Rawat, Sengupta and Sitaram.
Study light ray transform in pseudo-Euclidean space, derive inversion formula, and prove stability.
problem Analyzing light ray transform in pseudo-Euclidean space.
method Investigate normal operator, derive inversion formula, analyze as Fourier Integral Operator.
result Derive an inversion formula and prove stability estimates.
Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing. This paper introduces BNet2, a simplified Butterfly-Net and inline with the conventional CNN. Moreover, a Fourier transform i…
The paper proposes a novel method for optimizing bounded functions using Fourier series and Ricci flow.
problem Optimizing bounded functions using Fourier series and Ricci flow.
method Approximating the initial manifold using Fourier series and center/boundary sampling. Iteratively evolving the manifold using geodesic hyper-spheres and inverse Ricci flow.
result The method allows for the optimization of high curvature regions and achieves potential global optima.
Study spherical Fourier transform on hypergeometric type harmonic manifolds.
problem Spherical Fourier transform on harmonic Hadamard manifolds.
method Representation of spherical functions by Gauss hypergeometric functions.
result Inversion formula, convolution rule, and Plancherel theorem are derived.
We extend the Fourier cosine method to discrete probability distributions, achieving faster convergence rates.
problem Extending Fourier cosine method to discrete probability distributions.
method Spectral filters and convergence rates analysis.
result Spectral filters achieve one order faster convergence rates than previously recognized.
Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
Analytical pricing formulas and Greeks are obtained for European and American basket put options using Mellin transforms. We assume assets are driven by geometric Brownian motion which exhibit correlation and pay a continuous dividend rate. A novel approach to numerical Mellin inversion is achieved via the fast Fourier…
The paper introduces a new volatility model using Fourier techniques for pricing and hedging.
problem Pricing and hedging of financial derivatives with stochastic volatility.
method A Fourier-based approach to price and hedge European and path-dependent options in a stochastic volatility model.
result The model includes and extends popular volatility models like Stein-Stein, Bergomi, and Heston.
The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.
problem Calibrating and pricing options in polynomial Ornstein-Uhlenbeck volatility models.
method Analyzes Fourier-Laplace transforms, connects to Riccati equations, and develops numerical schemes.
result Establishes existence and solution for Riccati equations and provides efficient numerical methods.
Random Fourier features model reconstructs wind fields from sparse measurements.
problem Reconstructing wind fields from limited data.
method Random Fourier features approximating velocity field with adaptive sampling.
result Random Fourier features model outperforms benchmarks.
FourNet approximates financial transition densities using Fourier transforms.
problem Approximating transition densities in finance with high accuracy.
method FourNet is a novel FFNN with Gaussian activation, learning from characteristic functions.
result FourNet can approximate transition densities arbitrarily well with finite neurons.
We consider the horospherical transform and its inversion in 3 examples of hyperboloids. We want to illustrate via these examples the fact that the horospherical inversion formulas can be directly extracted from the classical Radon inversion formula. In a more broad context, this possibility reflects the fact that the …
EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.
problem Parameter estimation and trajectory reconstruction for noisy, sparse, nonlinear ODE systems.
method EFiGP integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework.
result EFiGP efficiently estimates ODE parameters and recovers trajectories from noisy data.
New bounds on ReLU networks for low-regular functions.
problem Bounding approximation error for ReLU networks on low-regular functions.
method Complexity analysis of Fourier features residual networks to ReLU networks.
result Approximation error bound proportional to target function norm and inversely proportional to network width and depth.
In this paper, we discuss the uniqueness in an integral geometry problem in a strongly convex domain. Our problem is related to the problem of finding a Riemannian metric by the distances between all pairs of the boundary points. For the proof, the problem is reduced to an inverse source problem for a kinetic equation …
We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential \levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential…
Researchers extend asymptotic analysis to Bergman projections with Gevrey weights.
problem Analyzing Bergman projections with Gevrey weights.
method Extending direct approach to semiclassical asymptotics to Gevrey weights using Fourier integral operators.
result Gevrey symbol amplitude of asymptotic Bergman projection with Gevrey weights and Gevrey-type growth rate.
iSTFTNet speeds up mel-spectrogram vocoders without sacrificing quality.
problem Efficiently converting mel-spectrograms to speech with minimal computation.
method Replaces convolutional layers with iSTFT after frequency dimension reduction.
result Significant reduction in computational cost with comparable quality.
Develops a new bivariate process for energy markets with improved simulation methods.
problem Modelling energy markets with stochastic delays and efficient simulations.
method Introduces a novel bivariate Normal Inverse Gaussian process and a path simulation scheme.
result Improves simulation efficiency for energy market models.
We establish several closed pricing formula for various path-independent payoffs, under an exponential Lévy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools from Mellin transform theory as well as from multidimensional complex analysis. Par…
Diffusion models tackle noisy inverse problems with posterior sampling.
problem Efficiently solving general noisy inverse problems.
method Approximation of posterior sampling for diffusion models.
result Diffusion models can handle various noise statistics and nonlinear problems.
A new model for pricing ultra-short-term options with complex volatility patterns.
problem Complex pricing of ultra-short-term options due to oscillations in implied volatility.
method Edgeworth++ model with nonparametric stochastic volatility and deterministic shift extension.
result Fast and accurate closed-form option pricing for ultra-short-term options.
A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined on a harmonic Hadamard manifold of hypergeometric type admits an inversion formula. A characterization of harmonic Hadamard manifold being of…
The article provides representations of exchange option prices under SVJD dynamics.
problem Modeling and pricing exchange options under stochastic volatility and jumps.
method Develops representations for European and American exchange options using SVJD dynamics and equivalent martingale measures.
result Derives integro-partial differential equations and representations for exchange option prices.
New integral theorems improve density function estimations.
problem Improving density function estimations.
method Integrals based on cyclic functions and Riemann sums, Fourier integral theorem, Monte Carlo methods, variational approach, Cauchy residue theorem.
result Optimal cyclic functions minimize square integrals, improving density estimations.
This paper explores deep learning for improving X-ray CT image reconstruction from undersampled data.
problem Improving image reconstruction from undersampled X-ray CT data.
method Analysis of classical and deep learning methods for solving inverse problems.
result Deep learning methods show promise in improving image quality from undersampled data.
Initialization of parameters in deep neural networks has been shown to have a big impact on the performance of the networks (Mishkin & Matas, 2015). The initialization scheme devised by He et al, allowed convolution activations to carry a constrained mean which allowed deep networks to be trained effectively (He et al.…
Solves wave equation on non-flat harmonic manifolds using Abel transform and Fourier analysis.
problem Wave equation on non-flat harmonic manifolds with specific curvature conditions.
method Explicit representation using inverse dual Abel transform and Fourier transform.
result Shows asymptotic Huygens principle and equidistribution of energy.
New PINN architectures learn high-frequency features using Fourier features.
problem PINNs struggle with high-frequency or multi-scale features.
method Employ spatio-temporal and multi-scale random Fourier features.
result Effective PINN models for multi-scale PDEs.
Established PFPPs in complete markets, solving integral equations.
problem Existence of Predictable Forward Performance Processes in complete markets.
method Solving a one-period integral equation using Fourier transform for tempered distributions.
result Closed-form solutions for PFPPs with inverse marginal functions that are completely monotonic.
HFNO enhances interpretability of turbulent flows through parallel wavenumber bin processing.
problem Opaque inner workings of Fourier Neural Operators (FNOs) hinder physical interpretability.
method Introduces HFNO, a novel FNO-based architecture that processes wavenumber bins in parallel, enhancing interpretability.
result HFNO decomposes turbulent flows across various scales, enabling increased interpretability and multiscale modeling.
Paper develops methods for estimating and simulating a Student-t Lévy regression model.
problem Estimation and simulation of Student-t Lévy process with arbitrary degrees of freedom.
method Develops a two-step estimation procedure and simulates increments using inverse Fourier transform.
result Efficient estimation and simulation methods for Student-t Lévy process.
Constructs smooth integrable magnetic systems on a two-torus.
problem Creating smooth magnetic systems on a two-torus with specific properties.
method Uses Nash-Moser implicit function theorem to find zeros of an action functional.
result Characterizes Zoll magnetic systems and proves their existence.
SURGIN uses generative models to infer subsurface flow data efficiently.
problem Inefficient and task-specific inversion methods for subsurface multiphase flow.
method SURGIN integrates U-FNO surrogate with SGM for zero-shot conditional generation.
result Decent inference of heterogeneous geological fields and flow dynamics with uncertainty quantification.
Researchers derive an analytic expression for Gaussian stochastic volatility models.
problem Analyzing rich autocorrelation structures and persistence in financial markets.
method Two different analytic derivations of the joint characteristic function.
result First analytic formulae for option pricing in rough volatility models.
Novel neural network layer improves long-range interactions in point clouds.
problem Efficiently treating long-range interactions in point clouds.
method Long-range convolutional (LRC)-layer that incorporates Fourier transforms.
result Global all-to-all convolution operation performed in nearly-linear time.
Develops flexible non-parametric ACFs using B-spline kernels.
problem Flexible modelling of the autocovariance function (ACF) in time-series, spatial, and spatio-temporal analysis.
method Derives the inverse Fourier transform of B-spline spectral bases to create a general class of non-parametric ACFs.
result Provides a provably dense, flexible, and general class of non-parametric ACFs for various types of processes.
New methods estimate multivariate shortfall risk more efficiently.
problem Estimating multivariate shortfall risk is computationally challenging.
method Combines Fourier inversion and RQMC sampling in frequency domain.
result Fourier RQMC methods outperform existing benchmarks.
Unified method for deriving ridgelet transforms for various neural network architectures.
problem Deriving closed-form expressions for ridgelet transforms in modern neural network architectures.
method Unified Fourier slice method to derive ridgelet transforms for diverse neural network types.
result Systematic method to derive ridgelet transforms for various neural network architectures.
Unified model for equity option pricing and interest-rate risk assessment.
problem Pricing short and medium-term equity options and interest-rate risk.
method Developed a stochastic modeling framework using Heston, Bates, and CIR models, calibrated using Fourier inversion and FFT.
result Calibration stability and convergence of parameter sets across models.
Closed-form formulas for path-independent options in a specific Lévy model.
problem Valuation of path-independent options in the exponential NIG model.
method Closed-form pricing formulas derived using a factorized representation in Mellin space and complex analysis.
result Valid closed-form formulas with quickly convergent series for various options.
Previous research has shown that computation of convolution in the frequency domain provides a significant speedup versus traditional convolution network implementations. However, this performance increase comes at the expense of repeatedly computing the transform and its inverse in order to apply other network operati…
Infinity-harmonic functions linked to IMCF clusters, revealing new properties in 2D.
problem Understanding properties of ∞-harmonic functions in 2D. method Relating ∞-harmonic functions to inverse mean curvature flow clusters and their po∞ limit. result New structural and regularity results for ∞-harmonic functions in 2D. We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total…
We introduce a multi-factor stochastic volatility model based on the CIR/Heston stochastic volatility process. In order to capture the Samuelson effect displayed by commodity futures contracts, we add expiry-dependent exponential damping factors to their volatility coefficients. The pricing of single underlying Europea…
The paper speeds up and improves pricing and calibration for the rough Heston model.
problem Improving the accuracy and speed of pricing vanilla options under the rough Heston model.
method Combining modified Adams method with SINH-acceleration method for Fourier inversion.
result The model implied vol surface is much flatter and fits market data poorly, indicating ghost calibration.