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Author
M. Decamps
M.J. Goovaerts
W. Schoutens
Year
2006
Title
Asymmetric skew Bessel processes and their applications to finance
Journal
Journal of Computational and Applied Mathematics
Volume | Issue number
186 | 1
Pages (from-to)
130-147
Number of pages
18
Document type
Article
Faculty
Faculty of Economics and Business (FEB)
Institute
Amsterdam School of Economics Research Institute (ASE-RI)
Abstract
In this paper, we extend the Harrison and Shepp's construction of the skew Brownian motion (1981) and we obtain a diffusion similar to the two-dimensional Bessel process with speed and scale densities discontinuous at one point. Natural generalizations to multi-dimensional and fractional order Bessel processes are then discussed as well as invariance properties. We call this family of diffusions asymmetric skew Bessel processes in opposition to skew Bessel processes as defined in Barlow et al. [On Walsh's Brownian motions, Séminaire de Probabilitiés XXIII, Lecture Notes in Mathematics, vol. 1372, Springer, Berlin, New York, 1989, pp. 275-293]. We present factorizations involving (asymmetric skew) Bessel processes with random time. Finally, applications to the valuation of perpetuities and Asian options are proposed.
URL
go to publisher's site
Language
Undefined/Unknown
Permalink
http://hdl.handle.net/11245/1.271246

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