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Symmetry Group Methods for Fundamental Solutions and Characteristic Functions

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This paper uses Lie symmetry group methods to analyse a class of partial differential equations of he form It is shown that when the drift function f is a solution of a family of Ricatti equations, then symmetry techniques can be used to find the characteristic functions and transition densities of the corresponding diffusion processes.Keywords: lie symmetry groups; green's functions; fundamental solutions; characteristic functions; transition densities; symmetry techniques

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  • Mark Craddock & Eckhard Platen, 2003. "Symmetry Group Methods for Fundamental Solutions and Characteristic Functions," Research Paper Series 90, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:90
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp90.pdf
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    1. Mark Craddock & David Heath & Eckhard Platen, 1999. "Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing," Research Paper Series 27, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Cited by:

    1. Eckhard Platen & Renata Rendek, 2009. "Exact Scenario Simulation for Selected Multi-dimensional Stochastic Processes," Research Paper Series 259, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Mark Craddock & Kelly A Lennox, 2006. "Lie Group Symmetries as Integral Transforms of Fundamental Solutions," Research Paper Series 183, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Jan Baldeaux & Eckhard Platen, 2012. "Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods," Papers 1204.1126, arXiv.org.

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