Improved convergence rate for the simulation of stochastic differential equations driven by subordinated Lévy processes
We consider the Euler approximation of stochastic differential equations (SDEs) driven by Lévy processes in the case where we cannot simulate the increments of the driving process exactly. In some cases, where the driving process Y is a subordinated stable process, i.e., Y=Z(V) with V a subordinator and Z a stable process, we propose an approximation Y by Z(Vn) where Vn is an approximation of V. We then compute the rate of convergence for the approximation of the solution X of an SDE driven by Y using results about the stability of SDEs.
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Volume (Year): 108 (2003)
Issue (Month): 1 (November)
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- Barndorff-Nielsen, Ole E. & Pérez-Abreu, Victor, 1999. "Stationary and self-similar processes driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 357-369, December.
- Marc Yor & Dilip B. Madan & Hélyette Geman, 2002. "Stochastic volatility, jumps and hidden time changes," Finance and Stochastics, Springer, vol. 6(1), pages 63-90.
- Hélyette Geman & Dilip B. Madan & Marc Yor, 2001. "Time Changes for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 79-96.
- Rubenthaler, Sylvain, 2003. "Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 311-349, February.
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