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Estimating multidimensional density functions using the Malliavin-Thalmaier formula

The Malliavin-Thalmaier formula was introduced for simulation of high dimensional probability density functions. But when this integration by parts formula is applied directly in computer simulations, we show that it is unstable. We propose an approximation to the Malliavin-Thalmaier formula. In this paper, we find the order of the bias and the variance of the approximation error. And we obtain an explicit Malliavin-Thalmaier formula for the calculation of Greeks in finance. The weights obtained are free from the curse of dimensionality.

Identiferoai:union.ndltd.org:PUCP/oai:tesis.pucp.edu.pe:123456789/96672
Date25 September 2017
CreatorsKohatsu Higa, Arturo, Yasuda, Kazuhiro
PublisherPontificia Universidad Católica del Perú
Source SetsPontificia Universidad Católica del Perú
LanguageEspañol
Detected LanguageEnglish
TypeArtículo
FormatPDF
SourcePro Mathematica; Vol. 21, Núm. 41-42 (2007); 61-106
RightsArtículo en acceso abierto, Attribution 4.0 International, https://creativecommons.org/licenses/by/4.0/

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