Multivariate Integral Perturbation Techniques - I (Theory)

TL;DR

This paper introduces a quasi-analytic perturbation expansion method for multivariate Gaussian and Student-t integrals, providing explicit second-order evaluations and discussing convergence and applications in finance.

Contribution

It develops a novel perturbation expansion approach for multivariate integrals, enabling easier computation and analysis of complex high-dimensional integrals in finance and statistics.

Findings

Explicit second-order perturbation expansion for multivariate integrals

Discussion on convergence and enhancement techniques like Pade approximants

Potential applications in financial modeling and risk assessment

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 Pade approximants. Brief comments on potential applications in finance are given, including options, models for credit risk and derivatives, and correlation sensitivities.