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Regular Strong Taylor Approximations with Jumps

  • Eckhard PlatenEmail author
  • Nicola Bruti-Liberati
Chapter
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Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 64)

Abstract

In this chapter we start to go beyond the work described in Kloeden & Platen (1999) on the numerical solution of SDEs. We now allow the driving noise of the SDEs to have jumps. We present regular strong approximations obtained directly from a truncated Wagner-Platen expansion with jumps. The term regular refers to the time discretizations used to construct these approximations. These do not include the jump times of the Poisson random measure, as opposed to the jump-adapted strong approximations that will be presented later in Chap. 8. A convergence theorem for approximations of a given strong order of convergence will be presented at the end of this chapter. The reader who aims to simulate a solution of an SDE with low jump intensity is referred directly to Chap. 8 which describes jump-adapted schemes that are convenient to use.

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References

  1. Kloeden, P. E. & Platen, E. (1999). Numerical Solution of Stochastic Differential Equations, Vol. 23 of Appl. Math., Springer. Third printing, (first edition (1992)). Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of Finance and Economics, Department of Mathematical SciencesUniversity of Technology, SydneyBroadwayAustralia

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