Numerical Stability

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


When simulating discrete-time approximations of solutions of SDEs, in particular martingales, numerical stability is clearly more important than higher order of convergence. The stability criterion presented is designed to handle both scenario and Monte Carlo simulation, that is, both strong and weak approximation methods. Stability regions for various schemes are visualized. The result being that schemes, which have implicitness in both the drift and the diffusion terms, exhibit the largest stability regions. Refining the time step size in a simulation can lead to numerical instabilities, which is not what one experiences in deterministic numerical analysis. This chapter follows closely Platen & Shi (2008).


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  1. Platen, E. & Shi, L. (2008). On the numerical stability of simulation methods for SDEs, Technical report, University of Technology, Sydney. QFRC Research Paper 234. 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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