Journal of Applied Probability

The explicit Laplace transform for the Wishart process

Alessandro Gnoatto and Martino Grasselli

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Abstract

We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral, which extends the original approach of Bru (1991). We compare our methodology with the alternative results given by the variation-of-constants method, the linearization of the matrix Riccati ordinary differential equation, and the Runge-Kutta algorithm. The new formula turns out to be fast and accurate.

Article information

Source
J. Appl. Probab., Volume 51, Number 3 (2014), 640-656.

Dates
First available in Project Euclid: 5 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1409932664

Digital Object Identifier
doi:10.1239/jap/1409932664

Mathematical Reviews number (MathSciNet)
MR3256217

Zentralblatt MATH identifier
1304.65008

Subjects
Primary: 65C30: Stochastic differential and integral equations
Secondary: 60H35: Computational methods for stochastic equations [See also 65C30] 91B70: Stochastic models

Keywords
Affine process Wishart process ordinary differential equation Laplace transform

Citation

Gnoatto, Alessandro; Grasselli, Martino. The explicit Laplace transform for the Wishart process. J. Appl. Probab. 51 (2014), no. 3, 640--656. doi:10.1239/jap/1409932664. https://projecteuclid.org/euclid.jap/1409932664


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