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
Kloeden, P. E. & Platen, E. (1999). Numerical Solution of Stochastic Differential Equations, Vol. 23 of Appl. Math., Springer. Third printing, (first edition (1992)).
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© 2010 Springer-Verlag Berlin Heidelberg
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Platen, E., Bruti-Liberati, N. (2010). Regular Strong Taylor Approximations with Jumps. In: Numerical Solution of Stochastic Differential Equations with Jumps in Finance. Stochastic Modelling and Applied Probability, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13694-8_6
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DOI: https://doi.org/10.1007/978-3-642-13694-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12057-2
Online ISBN: 978-3-642-13694-8
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