Lie Symmetries and Invariant Solutions for Geometric Mean Reversion

Summary

The document applies Lie symmetry analysis to a Feynman–Kac equation associated with a classical geometric mean reversion process. The process is presented as a model for short-term interest rate dynamics, with a supply response to price increases offered as a reason it may represent some investment settings more realistically than geometric Brownian motion.

The analysis derives the equation’s infinitesimal symmetry algebra and corresponding one-parameter groups, then uses an optimal system of one-dimensional subalgebras to construct invariant solutions. The excerpt describes the mathematical approach and outputs, but provides no specific solution forms, empirical tests, or quantitative evidence. Its relevance to trading is therefore mainly methodological: it concerns model structure and solution techniques rather than a tested trading strategy.

Key ideas

• Lie symmetry methods are applied to a Feynman–Kac equation for geometric mean reversion.
• The process is framed as a model for short-term interest rates.
• The analysis derives infinitesimal symmetries and their associated one-parameter groups.
• An optimal system of subalgebras is used to construct invariant solutions.
• The excerpt gives no empirical validation or trading performance evidence.

Tags

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


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









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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