New Paper: Multivariate Integral Perturbation Techniques - I (Theory)

Attached is my new paper MULTIVARIATE INTEGRAL PERTURBATION TECHNIQUES - I (THEORY). The paper introduces the theory for a perturbation method for evaluating an N-dimensional multivariate Gaussian integral, breaking it down into a sum of one-dimensional integrals. Numerical aspects are being examined, and will appear in a forthcoming paper.

This paper is now published: International Journal of Theoretical & Applied Finance, Vol 10, No. 8, pp. 1287-1304 (Dec. 2007)

Here is the abstract:

ABSTRACT: We present a quasi-analytic perturbation expansion for multivariate N-dimensional Gaussian integrals. The perturbation expansion is an infinite series of lower-dimensional integrals (one-dimensional in the simplest approximation). This perturbative idea can also be applied to multivariate Student-t integrals. We evaluate the perturbation expansion explicitly through 2nd order, and discuss the convergence, including enhancement using Padé approximants. Brief comments on potential applications in finance are given, including options, models for credit risk and derivatives, and correlation sensitivities.

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http://www.wilmott.com/blogs/jandash/enclosures/DASH Multivariate Integral Perturbative Techniques I Theory Sept06 R2 posted.pdf

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