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Deterministic multi-level algorithms for infinite-dimensional integration on
- Source :
-
Journal of Complexity . Jun2011, Vol. 27 Issue 3/4, p331-351. 21p. - Publication Year :
- 2011
-
Abstract
- Abstract: Pricing a path-dependent financial derivative, such as an Asian option, requires the computation of , the expectation of a payoff function , that depends on a Brownian motion . Employing a standard series expansion of the latter problem is equivalent to the computation of the expectation of a function of the corresponding i.i.d. sequence of random coefficients. This motivates the construction and the analysis of algorithms for numerical integration with respect to a product probability measure on the sequence space . The class of integrands studied in this paper is the unit ball in a reproducing kernel Hilbert space obtained by superposition of weighted tensor product spaces of functions of finitely many variables. Combining tractability results for high-dimensional integration with the multi-level technique we obtain new algorithms for infinite-dimensional integration. These deterministic multi-level algorithms use variable subspace sampling and they are superior to any deterministic algorithm based on fixed subspace sampling with respect to the respective worst case error. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0885064X
- Volume :
- 27
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Journal of Complexity
- Publication Type :
- Academic Journal
- Accession number :
- 60223498
- Full Text :
- https://doi.org/10.1016/j.jco.2010.08.001