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Bessel bridges decomposition with varying dimension. Applications to finance

Author

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  • Gabriel Faraud

    (WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] - FVB - Forschungsverbund Berlin e.V. (FVB))

  • Stéphane Goutte

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider a class of stochastic processes containing the classical and well-studied class of Squared Bessel processes. Our model, however, allows the dimension be a function of the time. We first give some classical results in a larger context where a time-varying drift term can be added. Then in the non-drifted case we extend many results already proven in the case of classical Bessel processes to our context. Our deepest result is a decomposition of the Bridge process associated to this generalized squared Bessel process, much similar to the much celebrated result of J. Pitman and M. Yor. On a more practical point of view, we give a methodology to compute the Laplace transform of additive functionals of our process and the associated bridge. This permits in particular to get directly access to the joint distribution of the value at t of the process and its integral. We finally give some financial applications to illustrate the panel of applications of our results.

Suggested Citation

  • Gabriel Faraud & Stéphane Goutte, 2015. "Bessel bridges decomposition with varying dimension. Applications to finance," Post-Print hal-00694126, HAL.
    • Handle: RePEc:hal:journl:hal-00694126
    DOI: 10.1007/s10959-013-0496-x
    Note: View the original document on HAL open archive server: https://hal.science/hal-00694126
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    References listed on IDEAS

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    1. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
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    Cited by:

    1. David Clancy, 2021. "The Gorin–Shkolnikov Identity and Its Random Tree Generalization," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2386-2420, December.

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