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arXiv · 2504.13094

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

Jin Zhang·Dapeng Gao
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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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BibTeXRIS

Jin Zhang, Dapeng Gao. 2025-04-17. Symmetry classification and invariant solutions of the classical geometric mean reversion process. https://doi.org/10.3934/dcdss.2024202

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