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Jump-Adapted Weak Approximations

  • Eckhard PlatenEmail author
  • Nicola Bruti-Liberati
Chapter
  • 4.7k Downloads
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 64)

Abstract

In this chapter we consider weak approximations constructed on jump-adapted time discretizations similar to those presented in Chap. 8. Since a jump-adapted discretization includes the jump times of the Poisson measure, we can use various approximations for the pure diffusion part between discretization points. Higher order jump-adapted weak schemes avoid multiple stochastic integrals that involve the Poisson random measure. Only multiple stochastic integrals with respect to time and Wiener processes, or their equivalents, are required. This leads to easily implementable schemes. It needs to be emphasized that jump-adapted weak approximations become computationally demanding when the intensity of the Poisson measure is high.

Keywords

Weak Convergence Time Step Size Euler Scheme Weak Order Weak Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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