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Exact pathwise simulation of multi-dimensional Ornstein–Uhlenbeck processes

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  • de la Cruz, H.
  • Jimenez, J. C

Abstract

The exact pathwise simulation of multidimensional Ornstein–Uhlenbeck processes is considered. We propose two procedures that allow the exact pathwise simulation of this type of processes and, simultaneously, the generation of the underlying Wiener trajectories from the same source of randomness. This is particularly important when both processes are system-components in larger stochastic models, for which the study of pathwise dynamics is required.

Suggested Citation

  • de la Cruz, H. & Jimenez, J. C, 2020. "Exact pathwise simulation of multi-dimensional Ornstein–Uhlenbeck processes," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    • Handle: RePEc:eee:apmaco:v:366:y:2020:i:c:s009630031930726x
    DOI: 10.1016/j.amc.2019.124734
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Buckwar, Evelyn & Sickenberger, Thorsten, 2011. "A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1110-1127.
    3. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    4. Li, Chenxu & Wu, Linjia, 2019. "Exact simulation of the Ornstein–Uhlenbeck driven stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 275(2), pages 768-779.
    5. 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 1-2007.
    6. D. Valenti & G. Augello & B. Spagnolo, 2008. "Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 443-451, October.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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