Modelling a financial system’s debts as a directed graph and simplifying them. Netting through a clearing party, a trust-constrained reduction algorithm, the fixed-cost variant as Subset Sum, and dependent debt as Minimum Cost Feedback Arc Set, with an NP-hardness reduction from Vertex Cover.

Turning diversification into a graph problem. Building a correlation graph from stock returns, casting a maximally diversified portfolio as Maximum Independent Set / Maximum Clique, and benchmarking exact Bron-Kerbosch enumeration against the Halldórsson-Boppana approximation on the S&P 500.

Testing the efficient market hypothesis by searching foreign-exchange tick data for arbitrage. Currencies become a gain graph, arbitrage becomes a negative cycle, the search is NP-hard, and four methods (exhaustive enumeration, ant colony optimization, Bellman-Ford, and Karp’s minimum mean weight cycle) are benchmarked on 2008 and 2012 tick data.