Reconstruction of density functions by sk-splines
Mathematical Finance
2014-04-22 v1
Abstract
Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an analytic extension into an appropriate tube and "bell-shaped" with rapidly decaying tails. Unfortunately, the domain of such functions is not compact which creates various technical difficulties. We solve interpolation problem on an infinite rectangular grid for a wide range of kernel functions and calculate explicitly their Fourier transform to obtain representations for the respective density functions.
Cite
@article{arxiv.1404.5271,
title = {Reconstruction of density functions by sk-splines},
author = {A. Kushpel and J. Levesley},
journal= {arXiv preprint arXiv:1404.5271},
year = {2014}
}