Bessel Bridges Decomposition with Varying Dimension: Applications to Finance

Gabriel Faraud () and Stéphane Goutte
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Gabriel Faraud: Weierstrass Institute for Applied Analysis and Stochastics (WIAS)

Journal of Theoretical Probability, 2014, vol. 27, issue 4, 1375-1403

Abstract: 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 to 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 with this generalized squared Bessel process, much similar to the much celebrated result of J. Pitman and M. Yor. From 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. In particular, this provides direct access to the joint distribution of the values at $$t$$ t of the process and its integral. We finally give some financial applications of our results.

Keywords: Squared Bessel process; Bessel bridges decomposition; Laplace transform; Lévy–Ito representation; Financial applications; 60G07; 60H35; 91B70 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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Working Paper: Bessel bridges decomposition with varying dimension. Applications to finance (2015)
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DOI: 10.1007/s10959-013-0496-x

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