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How Lie Group Symmetries May Shape Financial Stochastic Models

Article Quant Q&A · Author: pyCthon
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Summary

The document asks how Lie groups might be applied in finance and offers a tentative analogy with their use in physics. The response suggests using a transformation group to impose invariance on a model, which can introduce additional terms into its equations, and speculates that a similar approach could be applied to financial stochastic processes.

This is a conceptual suggestion rather than a worked method. The question points to research papers and graduate coursework, but the answer says it has not examined those papers. It provides no specific financial model, derivation, application, or evidence of practical results. Readers should treat the proposed connection as an intuition about possible modeling tools, not as an established trading technique.

Key ideas

  • Lie groups can describe transformations under which a model is intended to remain invariant.
  • The response draws an analogy between symmetry-based modeling in physics and financial stochastic processes.
  • The answer only proposes that this approach might add terms to financial equations.
  • No concrete financial application or supporting derivation is provided.

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# application of lie groups in finance


# application of lie groups in finance












Can some one kindly go over some of the applications and use of Lie groups in finance? The math is very rigorous and I don't fully understand it or the potential it could have.

Let me share some examples with you, I'm sure there are many more. There even is a financial math graduate program in Europe where there is required course work that teaches Lie groups.

http://www.sciencedirect.com/science/article/pii/S0096300308009156

http://math.sut.ac.th/school/faculty/sergey/filespublic/2006/SrihirunMeleshkoSchultz2006_I.pdf

http://www.phy.cuhk.edu.hk/~cflo/Finance/papers/publications/lie_QF.pdf

## Answer by microcosme (score 3)

https://quant.stackexchange.com/a/3793

I didn't read the papers you linked but I can understand that lie groups may be used much as there are used in quantum field theories to build up gauge theories for interaction of particles. The purpose is to have a model that is invariant according to a given transformation group. This introduce interaction terms in the equations.

I can imagine that the same technique can be used in financial stochastic processes to force the introduction of new terms in the equations.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.