Abstract
The Hammersley–Clifford theorem states the equivalence between Markov and Gibbs random fields. The Markov property is a kind of ‘locality’ while the Gibbs property is a kind of ‘factorization’. We speculate that a generalization to gauge fields on graphs is possible. Such a generalization could provide a justification for using Gibbs measures in the application of gauge theories to finance.
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Notes
- 1.
To avoid going into financial definitions, this is anything that can be traded, goods, services, financial instruments.
- 2.
It is standard in finance to ignore in first approximation any ‘friction’ or ‘cost of trading’ like taxes, buy/sell spreads, etc.
- 3.
The price of any tradable thing is the connection on the edge between this thing and the corresponding currency.
- 4.
This term is not standard an could be in conflict with other usages but lets adopt it for the moment.
- 5.
We are borrowing the term form lattice gauge theory but now a plaquette is a 2-cell bounded by several edges and not necessarily a square bounded by four edges.
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Ganchev, A. (2018). About Markov, Gibbs, ... Gauge Theory ... Finance. In: Dobrev, V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 . LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 263. Springer, Singapore. https://doi.org/10.1007/978-981-13-2715-5_28
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