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Symmetry group methods for fundamental solutions

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Abstract

This paper uses Lie symmetry group methods to study PDEs of the form We show that when the drift function f is a solution of a family of Ricatti equations, then symmetry techniques can be used to find a fundamental solution.

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  • Mark Craddock & Eckhard Platen, 2004. "Symmetry group methods for fundamental solutions," Published Paper Series 2004-6, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    • Handle: RePEc:uts:ppaper:2004-6
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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. Alexander Lipton, 2024. "Hydrodynamics of Markets:Hidden Links Between Physics and Finance," Papers 2403.09761, arXiv.org.
    3. Craddock, Mark & Grasselli, Martino, 2020. "Lie symmetry methods for local volatility models," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3802-3841.
    4. Martino Grasselli, 2017. "The 4/2 Stochastic Volatility Model: A Unified Approach For The Heston And The 3/2 Model," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1013-1034, October.
    5. 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.
    6. Mark Craddock & Eckhard Platen, 2009. "On Explicit Probability Laws for Classes of Scalar Diffusions," Research Paper Series 246, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Eckhard Platen, 2025. "Information-minimizing stationary financial market dynamics," Papers 2507.18395, arXiv.org.
    8. Oraby, T. & Suazo, E. & Arrubla, H., 2023. "Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    9. Jan Baldeaux & Eckhard Platen, 2012. "Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods," Papers 1204.1126, arXiv.org.
    10. Mark Craddock, 2017. "Integral Transform and Lie Symmetry Methods for Scalar and Multi-Dimensional Diffusions," Research Paper Series 380, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Shunwei Zhu & Bo Wang, 2019. "Unified Approach for the Affine and Non-affine Models: An Empirical Analysis on the S&P 500 Volatility Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1421-1442, April.
    12. Mark Craddock & Martino Grasselli, 2016. "Lie Symmetry Methods for Local Volatility Models," Research Paper Series 377, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Alexander Lipton, 2023. "Kelvin Waves, Klein-Kramers and Kolmogorov Equations, Path-Dependent Financial Instruments: Survey and New Results," Papers 2309.04547, arXiv.org.

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