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Symmetry classification and invariant solutions of the classical geometric mean reversion process

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  • Jin Zhang
  • Dapeng Gao

Abstract

Based on the Lie symmetry method, we investigate a Feynman-Kac formula for the classical geometric mean reversion process, which effectively describing the dynamics of short-term interest rates. The Lie algebra of infinitesimal symmetries and the corresponding one-parameter symmetry groups of the equation are obtained. An optimal system of invariant solutions are constructed by a derived optimal system of one-dimensional subalgebras. Because of taking into account a supply response to price rises, this equation provides for a more realistic assumption than the geometric Brownian motion in many investment scenarios.

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  • Jin Zhang & Dapeng Gao, 2025. "Symmetry classification and invariant solutions of the classical geometric mean reversion process," Papers 2504.13094, arXiv.org.
    • Handle: RePEc:arx:papers:2504.13094
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    File URL: http://arxiv.org/pdf/2504.13094
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