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Abstract Algebraic and Related Frameworks in Finance

Article Quant Q&A · Author: SlavicDoomer
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Summary

The document surveys ways abstract algebra and neighboring mathematical frameworks have been applied to economics, finance, and accounting. It mentions quantum mechanics and field theory in interest rate research, Lie groups for interest rate models, category theory as a lens on credit and law, and group theory applied to double-entry accounting. It also points to fractional calculus and financial processes as related areas.

The examples are presented as references and avenues for further reading, rather than as a worked method or trading strategy. The answer explicitly cautions that these approaches may deepen conceptual understanding without having a clear practical application. It gives no empirical results, implementation details, or comparison of the cited approaches, so readers would need to consult the referenced books and papers to assess their assumptions and usefulness.

Key ideas

  • Abstract algebra has been explored as a framework for understanding some financial structures and models.
  • Quantum field theory and Lie groups have been applied to interest rate research.
  • Category theory has been proposed as a lens on credit, law, and finance.
  • Group theory has been used to model double-entry accounting.
  • The cited work is exploratory and does not establish practical trading applications.

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Full text
# Abstract algebra in economics and finance


# Abstract algebra in economics and finance












Are there any applications of abstract algebra (group theory, rings, fields etc.) in any branch of either economics or finance?

## Answer by Dimitri Vulis (score 7)

https://quant.stackexchange.com/a/53707

Yes, I've seen some interesting papers that improve one's insight into how things work, even if it is not clearly applicable to practice.

Belal Ehsan Baaquie published several books on applications of quantum mechanics and quantum field theory to finance, particularly interest rates. They're definitely fun to read. The most recent one is Quantum Field Theory for Economics and Finance (2018).

There was a related question here (not answered) a few years ago about using Lie Groups for interest rates. The paper Park, Chun, Han, Webber, Interest rate models on Lie groups is an example of this.

There have been attemps to view credit from the category theory viewpoint, for example Joseph Tanega. Default Invariance, A Naïve Category Theory of Law and Finance.

Not quite finance, but Algebraic Models for Accounting Systems by Nehmer, Perez, Robinson, Rambaud explores a group-theoretic view of double-entry accounting.

Not quite modern algrebra, but related:

Fractional Calculus and Fractional Processes with Applications to Financial Economics by Fallahgoul, Focardi, Fabozzi.

Edit: a recent paper links financial markets and topology: https://www.pm-research.com/content/iijpormgmt/early/2026/06/19/jpm2026038

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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