Jürgen Hartinger: Quasi Monte Carlo methods for unbounded integrands and its applications to financial mathematics

The estimation of key data in realistic financial models requires fast and stable algorithms for the numerical evaluation of highdimensional integration problems. After a short introduction in modern financial models, we show that various integrands of practial interest are unbounded and therefor not of bounded variation in the sense of Hardy and Krause, such that the (asymptotic) superiortiy of QMC over MC is not assured by the classical Koksma-Hlawka Theorem. The effect of unbounded integrands on the integration error can depend on subtle properties of the QMC sequence. The analysis of this properties yields to several numbertheoretic problems, which are discussed in the end.

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