Computing Tarski Fixed Points in Financial Networks

Battle Count: 65

This paper is primarily about financial network clearing and systemic risk rather than quantitative trading strategies. While it addresses financial networks and debt relationships, it does not involve trading signals, portfolio construction, market microstructure, or algorithmic execution. The claims trading component is about network adjustment for liquidity, not about trading strategies. The relevance is indirect - understanding systemic risk and clearing mechanisms could inform risk management in trading portfolios.

The algorithm involves multiple components: SCC computation on active graphs, solving linear programs (Flood-LP and Increase-LP), computing eigenvectors via Perron-Frobenius theorem, handling piecewise-linear payment function phases, managing default cost adjustments with auxiliary banks, and iterative asset injection. The LP formulations require careful construction, and the phase-based approach for piecewise-linear functions adds complexity. The claims trading algorithm combines binary search with LP maximization. Overall, this is a sophisticated algorithmic contribution requiring strong background in combinatorial optimization and linear programming.

The paper provides complete mathematical proofs, algorithm pseudocode (Algorithm 1), and detailed LP formulations. However, no implementation code or experimental validation is provided. The theoretical results are self-contained with full proofs, making verification possible but requiring significant mathematical expertise. No reference implementation or test instances are available.