Explaining Effective Low-Dimensionality

Andrew Dickinson ()
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Andrew Dickinson: University of Oxford, Mathematical Institute

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, pp 97-112 from Springer

Abstract: Summary It has been proposed by Owen et al. [CMO97,LO02] that the surprising efficacy of quasi-Monte Carlo methods, when applied to certain high-dimensional integrands arising in mathematical finance, results from the integrands being effectively low-dimensional in the superposition sense. In this paper, mathematical results are presented which relate effective low-dimensionality with the structure of the underlying stochastic differential equation.

Keywords: Brownian Bridge; Asian Option; Rough Path; Unit Hypercube; Risk Neutral Probability Measure (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-31186-7_7

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DOI: 10.1007/3-540-31186-6_7

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