Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling

DOI10.1016/J.CAM.2015.02.023zbMath1317.65005arXiv1408.4609OpenAlexW1970691395MaRDI QIDQ2345677

Josef Dick, Johann S. Brauchart, Lou Fang

Publication date: 22 May 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.4609

zbMATH Keywords

option pricingspherequasi-Monte Carlo methodsreproducing kernel Hilbert spacenumerical testStolarsky's invariance principleLambert transformSobol' pointsspherical cone discrepancy

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Monte Carlo methods (65C05) Microeconomic theory (price theory and economic markets) (91B24) Irregularities of distribution, discrepancy (11K38)

Related Items (6)

Equidistributed icosahedral configurations on the sphere ⋮ Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness ⋮ Projection pursuit based tests of normality with functional data ⋮ Theory of generalized discrepancies on a ball of arbitrary finite dimensions and algorithms for finding low-discrepancy point sets ⋮ Hyperuniform point sets on the sphere: deterministic aspects ⋮ Distributing many points on spheres: minimal energy and designs

Uses Software

• DLMF

Cites Work

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• A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness
• Fast orthogonal transforms and generation of Brownian paths
• Scrambling Sobol' and Niederreiter-Xing points
• On the \(L_2\)-discrepancy for anchored boxes
• A lower bound for the worst-case cubature error on spheres of arbitrary dimension
• Spherical harmonics
• Optimal lower bounds for cubature error on the sphere \(S^2\)
• A simple proof of Stolarsky’s invariance principle
• Good Path Generation Methods in Quasi-Monte Carlo for Pricing Financial Derivatives
• Enhancing Quasi-Monte Carlo Methods by Exploiting Additive Approximation for Problems in Finance
• Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction
• QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
• The mean square discrepancy of randomized nets
• A generalized discrepancy and quadrature error bound
• Monte Carlo Variance of Scrambled Net Quadrature
• Variance with alternative scramblings of digital nets
• Sums of Distances Between Points on a Sphere. II
• Theory of Reproducing Kernels

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