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An adaptive Monte Carlo integration algorithm with general division approach

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  • Alrefaei, Mahmoud H.
  • Abdul-Rahman, Houssam M.

Abstract

We propose an adaptive Monte Carlo algorithm for estimating multidimensional integrals over a hyper-rectangular region. The algorithm uses iteratively the idea of separating the domain of integration into 2ssubregions. The proposed algorithm can be applied directly to estimate the integral using an efficient way of storage. We test the algorithm for estimating the value of a 30-dimensional integral using a two-division approach. The numerical results show that the proposed algorithm gives better results than using one-division approach.

Suggested Citation

  • Alrefaei, Mahmoud H. & Abdul-Rahman, Houssam M., 2008. "An adaptive Monte Carlo integration algorithm with general division approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(1), pages 49-59.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:1:p:49-59
    DOI: 10.1016/j.matcom.2007.09.009
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    References listed on IDEAS

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    1. Lars O. Dahl, 2003. "An Adaptive Method For Evaluating Multidimensional Contingent Claims: Part I," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 301-316.
    2. Lars O. Dahl, 2003. "An Adaptive Method For Evaluating Multidimensional Contingent Claims: Part Ii," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 327-353.
    3. Karaivanova, Aneta & Dimov, Ivan, 1998. "Error analysis of an adaptive Monte Carlo method for numerical integration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 201-213.
    4. Usabel, Miguel A., 1998. "Applications to risk theory of a Monte Carlo multiple integration method," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 71-83, October.
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