Integral Equations, Quasi-Monte Carlo Methods and Risk Modeling

  • Michael PreischlEmail author
  • Stefan Thonhauser
  • Robert F. Tichy


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.



The authors are supported by the Austrian Science Fund (FWF) Project F5510 (part of the Special Research Program (SFB) “Quasi-Monte Carlo Methods: Theory and Applications”).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Michael Preischl
    • 1
    Email author
  • Stefan Thonhauser
    • 1
  • Robert F. Tichy
    • 1
  1. 1.Institute of Analysis and Number TheoryGraz University of TechnologyGrazAustria

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