Integral Transform and Lie Symmetry Methods for Scalar and Multi-Dimensional Diffusions

Mark Craddock
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Mark Craddock: School of Mathematical and Physical Sciences, University of Technology Sydney

No 380, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: In this paper we demonstrate the various ways in which Lie symmetry group and integral transform methods can be combined and applied to solve some important types of problems in the theory of diffusion processes. We may compute various kinds of transition probability densities, as well as densities for diffusions which are conditioned to be either reflecting or absorbed at some boundary. Reflection and absorption for squared Bessel processes on the line x = a is studied. We also show how various first hitting times may be computed. We study some higher dimensional diffusions and show how transform methods can be used to extend some one dimensional results to higher dimensions. We also produce a general formula for the sums of certain one dimensional processes. Finally, we introduce what seems to be a new class of processes which have nearly exact densities.

Keywords: Lie symmetry groups; fundamental solutions; transition densities (search for similar items in EconPapers)
Pages: 49 pages
Date: 2017-05-01
New Economics Papers: this item is included in nep-dcm
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Persistent link: https://EconPapers.repec.org/RePEc:uts:rpaper:380

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