Minimizing Effective Dimension Using Linear Transformation

Junichi Imai () and Ken Seng Tan ()
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Junichi Imai: Iwate Prefectural University, Faculty of Policy Studies
Ken Seng Tan: University of Waterloo, Department of Statistics and Actuarial Science

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2002, 2004, pp 275-292 from Springer

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.

Keywords: Principal Component Analysis; Monte Carlo; Linear Transformation; Dimension Reduction; Effective Dimension (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18743-8_16

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DOI: 10.1007/978-3-642-18743-8_16

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