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I am particularly interested in the dependence of profit on the path length (the number of intermediate currencies) and graphical models / algorithms. More specifically:

  1. How can we model currency disequilibrium? Are the paths with more intermediate currencies more likely to be profitable?

  2. What graph algorithms work and which don't? There seem to be contradictory statements about this. In particular, can we find all the profitable paths, or only the best path? Do the algorithms that do work require pre-specifying the number of currencies?

I will appreciate tips and reading recommendations. I have no background in finance, but my mathematical background is quite solid (PhD in physics.)

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    $\begingroup$ FWIW finding a circular arbitrage is equivalent to finding a negative cycle in a directed graph. Graph Theory provides algorithms for this task. Example medium.com/@anilpai/… I don't know of any specific Finance literature on this problem. $\endgroup$
    – noob2
    Oct 3 '20 at 15:27
  • $\begingroup$ Indeed, I understand the idea. I am looking for something more mathematically solid. Perhaps I will expand the question. $\endgroup$
    – Roger Vadim
    Oct 3 '20 at 16:00
  • $\begingroup$ @Vadim Are you acquainted with tropical mathematics? $\endgroup$
    – Rodrigo de Azevedo
    Oct 4 '20 at 11:10
  • $\begingroup$ @RodrigodeAzevedo No... but I did encounter this term in this context and thought it was just an outlier. Could you tell me a bit more? $\endgroup$
    – Roger Vadim
    Oct 4 '20 at 11:32
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    $\begingroup$ @Vadim Some graph algorithms can be written in terms of tropical linear algebra. Take a look at this. $\endgroup$
    – Rodrigo de Azevedo
    Oct 4 '20 at 11:47

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