arXiv research

The paper introduces new methods for Asian option pricing using Laguerre quadrature.

The paper approximates CARMA models for option pricing.

Approximates smooth surfaces using Laguerre geometry meshes.

Approximates surfaces using Laguerre geometry with spherical faces.

Laguerre geometry of surfaces in $\R^3$ is given in the book of Blaschke [1], and have been studied by E.Musso and L.Nicolodi [5], [6], [7], B. Palmer [8] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in $\R^n$. For any umbilical free hypersurface $x: M\to\R^n$ with non-zero …

A Laguerre minimal surface is an immersed surface in the Euclidean space being an extremal of the functional \int (H^2/K - 1) dA. In the present paper, we prove that the only ruled Laguerre minimal surfaces are up to isometry the surfaces R(u,v) = (Au, Bu, Cu + D cos 2u) + v (sin u, cos u, 0), where A, B, C, D are fixe…

The study of Laguerre isotropic hypersurfaces with rigidity and isoparametric properties.

In this paper we show that a Dupin hypersurface with constant Möbius curvatures is Möbius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere. We also show that a Dupin hypersurface with constant Laguerre curvatures is Laguerre equivalent to a flat L…

This paper connects Laguerre minimal surfaces to Weierstrass representations.

This exposition gives an introduction to the theory of surfaces in Laguerre geometry and surveys some results, mostly obtained by the authors, about three important classes of surfaces in Laguerre geometry, namely L-isothermic, L-minimal, and generalized L-minimal surfaces. The quadric model of Lie sphere geometry is a…

Spinor representation in isotropic space via Laguerre geometry.

A new method for pricing derivatives using self-exciting dynamics and finite-difference transforms.

A Laguerre geometric local characterization is given of L-minimal surfaces and Laguerre deformations (T-transforms) of L-minimal isothermic surfaces in terms of the holomorphicity of a quartic and a quadratic differential. This is used to prove that, via their Laguerre Gauss maps, the T-transforms of L-minimal isotherm…

Motivated by the study of wave fronts in anisotropic media, we propose an incidence geometry of anisotropic spheres in a Finsler-Minkowski space. An anisotropic version of the Laguerre functional is considered. In some circumstances, this functional can be used to determine that two wavefronts observed at distinct time…

We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski $3$-space. We describe the geometry of null curves (Cartan frame, pseudo-arc parameter, pseudo-torsion, pairs of associated curves) in terms of the curvature of the correspon…

New quadrature method using randomly pivoted Cholesky outperforms existing techniques.

In a recent significant advance, using Laguerre series, the valuation of Asian options has been reduced by Dufresne to computing the negative moments of Yor's accumulation processes. For these he has given functional recursion rules whose probabilistic structure has been the object of intensive recent studies of Yor an…

We develop Fourier methods to expand translation-invariant kernels.

Bayesian quadrature uses probabilistic models for estimating intractable integrals.

SOBER optimizes and quadrates efficiently in parallel for diverse tasks.

This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We pr…

Improved Gaussian Process regression using TQFF over RFF and Gaussian QFF.

New representations for discrete surfaces derived from dual transforms.

We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the two kernels, along with DPP machinery, leads to relatively tight bounds on the qua…

Bayesian quadrature improves integration efficiency with invariant priors.

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior varianc…

Improved kernel quadrature with convex weights using subsampling.

We give an elaborated treatment of discrete isothermic surfaces and their analogs in different geometries (projective, Möbius, Laguerre, Lie). We find the core of the theory to be a novel projective characterization of discrete isothermic nets as Moutard nets. The latter belong to projective geometry and are nets with …

A new type of quadrature is developed. The Gaussian quadrature, for a given measure, finds optimal values of a function's argument (nodes) and the corresponding weights. In contrast, the Lebesgue quadrature developed in this paper, finds optimal values of function (value-nodes) and the corresponding weights. The Gaussi…

The sigma-point filters, such as the UKF, which exploit numerical quadrature to obtain an additional order of accuracy in the moment transformation step, are popular alternatives to the ubiquitous EKF. The classical quadrature rules used in the sigma-point filters are motivated via polynomial approximation of the integ…

In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but it exactly integrates the polynomials of both positive and negative orders. Using…

We present a procedure which allows one to integrate explicitly the class of checkerboard IC-nets which has recently been introduced as a generalisation of incircular (IC) nets. The latter class of privileged congruences of lines in the plane is known to admit a great variety of geometric properties which are also pres…

Adaptive Bayesian quadrature (ABQ) is a powerful approach to numerical integration that empirically compares favorably with Monte Carlo integration on problems of medium dimensionality (where non-adaptive quadrature is not competitive). Its key ingredient is an acquisition function that changes as a function of previou…

The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable…

Unified quadrature framework for large-scale kernel machines.

This paper introduces repulsive Monte Carlo methods for computing the sliced Wasserstein distance.

Novel approach for estimating conditional expectations using Bayesian quadrature.

New Fourier features improve high-precision approximation in large-scale problems.

Improved Nyström approximation for kernel quadrature with theoretical guarantees.

Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for …

Parallelized Bayesian quadrature improves sample efficiency and inference.

Adaptive quadrature improves Bayesian inference through active learning.

A new method calculates accurate SABR model option prices and deltas.

DBQPG improves policy gradient estimation with fewer samples.

Improved kernel herding algorithm for faster quadrature rule convergence.

Bayesian quadrature improves conformal prediction for better risk assessment.

Efficiently marginalizes over Gaussian Process kernels for better model flexibility and uncertainty.