Integral Equations, Quasi-Monte Carlo Methods and Risk Modeling

Michael Preischl (), Stefan Thonhauser () and Robert F. Tichy ()
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Michael Preischl: Graz University of Technology, Institute of Analysis and Number Theory
Stefan Thonhauser: Graz University of Technology, Institute of Analysis and Number Theory
Robert F. Tichy: Graz University of Technology, Institute of Analysis and Number Theory

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 1051-1074 from Springer

Abstract: 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: Quasi-Monte Carlo Methods; Aistleitner; Hardy-Krause Variation; Gerber-Shiu Function; Discounted Penalty Function (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-72456-0_47

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DOI: 10.1007/978-3-319-72456-0_47

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