Work

Malliavin-Stein method for variance-gamma approximation on Wiener space

Year: 2015

Type: article

Abstract: We combine Malliavin calculus with Stein's method to derive bounds for the Variance-Gamma approximation of functionals of isonormal Gaussian processes, in particular of random variables living inside a fixed Wiener chaos induced by such a process. The bounds are presented in terms of Malliavin operators and norms of contractions. We show that a sequence of distributions of random variables in the second Wiener chaos converges to a Variance-Gamma distribution if and only if their moments of order two to six converge to that of a Variance-Gamma distributed random variable (six moment theorem). Moreover, simplified versions for Laplace or symmetrized Gamma distributions are presented. Also multivariate extensions and a universality result for homogeneous sums are considered.

Source: Electronic Journal of Probability

DOI: 10.1214/ejp.v20-4136

Authors: Peter Eichelsbacher, Christoph Thäle

Institution: Ruhr University Bochum

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: Deutsche Forschungsgemeinschaft