Integral equations, quasi-Monte Carlo methods and risk modelling
Probability
2017-07-13 v1
Abstract
We survey a QMC approach to integral equations and develop some new applications to risk modeling. In particular, a rigorous error bound derived from Koksma-Hlawka type inequalities is achieved for certain expectations related to the probability of ruin in Markovian models. The method is based on a new concept of isotropic discrepancy and its applications to numerical integration. The theoretical results are complemented by numerical examples and computations.
Keywords
Cite
@article{arxiv.1707.03655,
title = {Integral equations, quasi-Monte Carlo methods and risk modelling},
author = {Michael Preischl and Stefan Thonhauser and Robert F. Tichy},
journal= {arXiv preprint arXiv:1707.03655},
year = {2017}
}