You have exchange rates between currencies. Can you start with one currency, make a series of exchanges, and end with more than you started?
This is arbitrage. Model currencies as nodes and exchange rates as edge weights. Convert rates to logarithms: . A profitable cycle becomes a negative cycle because .
Run Bellman-Ford to detect the negative cycle. If found, you can profit by following the cycle. The logarithm trick converts multiplication to addition, making the problem fit Bellman-Ford.