A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Two-layer networks struggle with high frequencies due to numerical and computational limitations.
The paper extends a method for numerical conformal mappings to surfaces using Laplace-Beltrami equations.
NGRC shows numerical instabilities with short lags and high-degree polynomials.
LightOn OPUs accelerate randomized numerical linear algebra, reducing computational costs.
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…
The second del Pezzo surface is known by work of Tian-Zhu and Wang-Zhu to admit a unique Kaehler-Ricci soliton. Applying a method described in hep-th/0703057, we use Ricci flow to numerically compute that soliton metric. We numerically compute the value of its Perelman entropy (or Gaussian density).
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation …
In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding on bounded convex domain in . We estimate the best constant by computing the corresponding extremal function using a verified numerical com…
New method calculates cut locus on surfaces without boundary.
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators of the braid group.
Optimal insurance policy for exponential utility maximization with convex premium calculation.
This paper numerically computes the topological and smooth invariants of Eschenburg spaces with small fourth cohomology group, following Kruggel's determination of the Kreck-Stolz invariants of Eschenburg spaces that satisfy condition C. The GNU GMP arbitrary-precision library is utilised.
With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing size, complexity and dimensionality of the problems. In particular, covariance mat…
Study numerical invariants for groups, computing for cyclic groups and surfaces.
Study identifies numerical signs of blow-up in hydrodynamic equations.
Verified numerics prove existence of a curvature solution with known symmetries.
Paper presents a fast algorithm for pricing Bermudan swaptions under the two-factor Hull-White model.
PHS optimizes hyperparameters in parallel for expensive computations.
Differentiable programming aids in solving differential equations and their sensitivities.
Twelve numerical methods for Poisson geometry concepts.
The defining equations for Killing vector fields and conformal Killing vector fields are overdetermined systems of PDE. This makes it difficult to solve the systems numerically. We propose an approach which reduces the computation to the solution of a symmetric eigenvalue problem. The eigenvalue problem is then solved …
An efficient adaptive direct numerical integration (DNI) algorithm is developed for computing high quantiles and conditional Value at Risk (CVaR) of compound distributions using characteristic functions. A key innovation of the numerical scheme is an effective tail integration approximation that reduces the truncation …
Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and computational improvements to the Rearrangement Algorithm for approximating wors…
GEORCE computes geodesics quickly and accurately.
Algorithm computes eigenvalues and eigenforms on Calabi-Yau threefolds.
CoLA automates efficient numerical linear algebra for complex matrix structures.
Researchers develop a numerical method to compute the index of self-shrinkers, finding it to be 5 for the Angenent torus.
The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.
In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock-out call options is presented. According to the well-known Black-Scholes framework, the price of option in each monitoring date could be calculate by computing a recursive integral formula upon the heat equati…
New method improves accuracy in computing implied volatility.
A new scheme for FBSDEs simplifies computation without Monte Carlo.
We give some detailed numerical information about extremal metrics on four different toric surfaces. These are sample of many other cases which can be treated using a computer programme outlined in the paper.
We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-paramete…
A deep learning model speeds up computation of numerous implied volatilities.
We present a numerical approach for solving the free boundary problem for the Black-Scholes equation for pricing American style of floating strike Asian options. A fixed domain transformation of the free boundary problem into a parabolic equation defined on a fixed spatial domain is performed. As a result a nonlinear t…
Improved method for numerical conformal mappings on complex 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…
We study q-holonomic sequences that arise as the colored Jones polynomial of knots in 3-space. The minimal-order recurrence for such a sequence is called the (non-commutative) A-polynomial of a knot. Using the "method of guessing", we obtain this polynomial explicitly for the K_p = (-2, 3, 3+2p) pretzel knots for p = -…
The matter of the stability for multi-asset American option pricing problems is a present remaining challenge. In this paper a general transformation of variables allows to remove cross derivative terms reducing the stencil of the proposed numerical scheme and underlying computational cost. Solution of a such problem i…
This paper deals with the evaluation of double line integrals of the squared exponential covariance function. We propose a new approach in which the double integral is reduced to a single integral using the error function. This single integral is then computed with efficiently implemented numerical techniques. The perf…
xVal tokenizes numbers continuously for better scientific model training.
Machine learning impacts computational math, offering new functions approximations.
Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems ranging from image classification/image recognition, speech recognition, time series analysis, game intelligence, and computational advertising to numerical approximations of partial differ…
GPU speeds up Monte Carlo simulations for large time steps.
Paper finds a method to compute fair risk-sharing rules.
New method uses tensor trains for efficient PDE approximation.
A machine learning approach to compute Black-Scholes prices with uncertain volatility.
The aim of this chapter is to show how option prices in jump-diffusion models can be computed using meshless methods based on Radial Basis Function (RBF) interpolation. The RBF technique is demonstrated by solving the partial integro-differential equation (PIDE) in one-dimension for the American put and the European va…