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The Explicit Laplace Transform for the Wishart Process

Part of: Mathematical economics Probabilistic methods, simulation and stochastic differential equations Stochastic analysis

Published online by Cambridge University Press:  30 January 2018

Alessandro Gnoatto  and
Martino Grasselli
Alessandro Gnoatto*
Affiliation:
LMU München
Martino Grasselli*
Affiliation:
Università di Padova, Pole Universitaire Léonard de Vinci and Quanta Finanza S.R.L.
*
∗ Postal address: Mathematisches Institut, LMU München, Theresienstrasse 39, D-80333 München, Germany. Email address: gnoatto@mathematik.uni-muenchen.de
∗∗ Postal address: Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy. Email address: grassell@math.unipd.it
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Abstract

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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.

Keywords

Affine processWishart processordinary differential equationLaplace transform

MSC classification

Primary: 65C30: Stochastic differential and integral equations
Secondary: 60H35: Computational methods for stochastic equations 91B70: Stochastic models
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 640 - 656
Copyright
© Applied Probability Trust 

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