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The approximation of multiple stochastic integrals

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Abstract

A method for approximating the multiple stochastic integrals appearing in stochaslic Taylor expansions is proposed. It is based on a series expansion of the Brownian bridge process. Some higher order time discrete approximations for the simulation of Ito processes using these approximate multiple stochastic integrals arc also included.

Suggested Citation

  • P. E. Kloeden & Eckhard Platen & I. W. Wright, 1992. "The approximation of multiple stochastic integrals," Published Paper Series 1992-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    • Handle: RePEc:uts:ppaper:1992-2
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    File URL: https://www.tandfonline.com/doi/abs/10.1080/07362999208809281
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    Cited by:

    1. Rydén, Tobias & Wiktorsson, Magnus, 2001. "On the simulation of iterated Itô integrals," Stochastic Processes and their Applications, Elsevier, vol. 91(1), pages 151-168, January.
    2. Lay Harold A. & Colgin Zane & Reshniak Viktor & Khaliq Abdul Q. M., 2018. "On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters," Monte Carlo Methods and Applications, De Gruyter, vol. 24(4), pages 309-321, December.
    3. Tocino, A., 2009. "Multiple stochastic integrals with Mathematica," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1658-1667.
    4. Malham, Simon J.A. & Wiese, Anke, 2014. "Efficient almost-exact Lévy area sampling," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 50-55.
    5. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
    6. Chenxu Li & Yu An & Dachuan Chen & Qi Lin & Nian Si, 2016. "Efficient computation of the likelihood expansions for diffusion models," IISE Transactions, Taylor & Francis Journals, vol. 48(12), pages 1156-1171, December.

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