Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations
This paper introduces a new class of numerical schemes for the pathwise approximation of solutions of stochastic differential equations (SDEs). The proposed family of strong predictor-corrector Euler methods are designed to handle scenario simulation of solutions of SDEs. It has the potential to overcome some of the numerical instabilities that are often experienced when using the explicit Euler method. This is of importance, for instance, in finance where martingale dynamics arise for solutions of SDEs with multiplicative diffusion coefficients. Numerical experiments demonstrate the improved asymptotic stability properties of the new symmetric predictor-corrector Euler methods.
|Date of creation:||01 Jun 2008|
|Date of revision:|
|Publication status:||Published as: Bruti-Liberati, N. and Platen, E., 2008, "Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations", Stochastics and Dynamics, 8(3), 561-581.|
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- Platen, Eckhard, 1995. "On weak implicit and predictor-corrector methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 69-76.
- Eckhard Platen, 2004.
"A Benchmark Approach to Finance,"
Research Paper Series
138, Quantitative Finance Research Centre, University of Technology, Sydney.
- Yoshihiro Saito & Taketomo Mitsui, 1993. "Simulation of stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer, vol. 45(3), pages 419-432, September.
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