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Improved convergence rate for the simulation of stochastic differential equations driven by subordinated Lévy processes

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  • Rubenthaler, Sylvain
  • Wiktorsson, Magnus
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    Abstract

    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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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 108 (2003)
    Issue (Month): 1 (November)
    Pages: 1-26

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    Handle: RePEc:eee:spapps:v:108:y:2003:i:1:p:1-26

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    Keywords: Stochastic differential equation Numerical approximation Convergence rate Lévy process Shot noise representation Subordination;

    References

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    1. 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.
    2. Rubenthaler, Sylvain, 2003. "Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 103(2), pages 311-349, February.
    3. Barndorff-Nielsen, Ole E. & Pérez-Abreu, Victor, 1999. "Stationary and self-similar processes driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 84(2), pages 357-369, December.
    4. Hélyette Geman & Dilip B. Madan & Marc Yor, 2001. "Time Changes for Lévy Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 11(1), pages 79-96.
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    Cited by:
    1. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1, June.

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