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Multilevel Monte Carlo by using the Halton sequence

Author

Listed:
  • Nagy Shady Ahmed
  • Wafa Mohamed

    (Engineering Mathematics and Physics Department, Engineering Faculty, Cairo University, Giza12613, Egypt)

  • El-Beltagy Mohamed A.

    (Engineering Mathematics and Physics Department, Engineering Faculty, Cairo University, Giza12613, Egypt)

Abstract

Monte Carlo (MC) simulation depends on pseudo-random numbers. The generation of these numbers is examined in connection with the Brownian motion. We present the low discrepancy sequence known as Halton sequence that generates different stochastic samples in an equally distributed form. This will increase the convergence and accuracy using the generated different samples in the Multilevel Monte Carlo method (MLMC). We compare algorithms by using a pseudo-random generator and a random generator depending on a Halton sequence. The computational cost for different stochastic differential equations increases in a standard MC technique. It will be highly reduced using a Halton sequence, especially in multiplicative stochastic differential equations.

Suggested Citation

  • Nagy Shady Ahmed & Wafa Mohamed & El-Beltagy Mohamed A., 2020. "Multilevel Monte Carlo by using the Halton sequence," Monte Carlo Methods and Applications, De Gruyter, vol. 26(3), pages 193-203, September.
    • Handle: RePEc:bpj:mcmeap:v:26:y:2020:i:3:p:193-203:n:2
    DOI: 10.1515/mcma-2020-2065
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    References listed on IDEAS

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    1. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
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