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Minimizing Effective Dimension Using Linear Transformation

In: Monte Carlo and Quasi-Monte Carlo Methods 2002

Author

Listed:
  • Junichi Imai

    (Iwate Prefectural University, Faculty of Policy Studies)

  • Ken Seng Tan

    (University of Waterloo, Department of Statistics and Actuarial Science)

Abstract

Summary In recent years, constructions based on Brownian bridge [11], principal component analysis [1], and linear transformation [7] have been proposed in the context of derivative pricing to further enhance QMC through dimension reduction. Motivated by [16, 18] and the ANOVA decomposition, this paper (i) formally justifies the dimension minimizing algorithm of Tan and Imai [7], and (ii) proposes a new formulation of linear transformation which explicitly reduces the effective dimension (in the truncation sense) of a function. Another new application of LT method to an interest rate model is considered. We establish the situation for which linear transformation method outperforms PCA.This method is not only effective on dimension reduction, it is also robust and can easily be extended to general diffusion processes.

Suggested Citation

  • Junichi Imai & Ken Seng Tan, 2004. "Minimizing Effective Dimension Using Linear Transformation," Springer Books, in: Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2002, pages 275-292, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18743-8_16
    DOI: 10.1007/978-3-642-18743-8_16
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