Integral equations, quasi-Monte Carlo methods and risk modelling

Michael Preischl; Stefan Thonhauser; Robert F. Tichy

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arXiv · 1707.03655

Integral equations, quasi-Monte Carlo methods and risk modelling

Michael Preischl·Stefan Thonhauser·Robert F. Tichy

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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.

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Michael Preischl, Stefan Thonhauser, Robert F. Tichy. 2017-07-12. Integral equations, quasi-Monte Carlo methods and risk modelling. https://arxiv.org/abs/1707.03655

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