Journal of Applied Probability

The explicit Laplace transform for the Wishart process

Alessandro Gnoatto and Martino Grasselli

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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

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

First available in Project Euclid: 5 September 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Affine process Wishart process ordinary differential equation Laplace transform


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.

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