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Integral equations, quasi-Monte Carlo methods and risk modeling. (English) Zbl 1405.65177
Dick, Josef (ed.) et al., Contemporary computational mathematics – a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Cham: Springer (ISBN 978-3-319-72455-3/hbk; 978-3-319-72456-0/ebook). 1051-1074 (2018).
Summary: 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.
For the entire collection see [Zbl 1398.65010].
MSC:
65R20 Numerical methods for integral equations
65C30 Numerical solutions to stochastic differential and integral equations
65C05 Monte Carlo methods
45B05 Fredholm integral equations
65C40 Numerical analysis or methods applied to Markov chains
65D30 Numerical integration
91B30 Risk theory, insurance (MSC2010)
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