Payment Scheduling in the Interval Debt Model

Stewart, Iain; Kutner, David; Friedetzky, Tom; Trehan, Amitabh; Mertzios, George

Abstract

The network-based study of financial systems has received considerable attention in recent years but has seldom explicitly incorporated the dynamic aspects of such systems. We consider this problem setting from the temporal point of view and introduce the Interval Debt Model (IDM) and some scheduling problems based on it, namely: Bankruptcy Minimization/Maximization, in which the aim is to produce a payment schedule with at most/at least a given number of bankruptcies; Perfect Scheduling, the special case of the minimization variant where the aim is to produce a schedule with no bankruptcies (that is, a perfect schedule); and Bailout Minimization, in which a financial authority must allocate a smallest possible bailout package to enable a perfect schedule. We show that each of these problems is NP-complete, in many cases even on very restricted input instances. On the positive side, we provide for Perfect Scheduling a polynomial-time algorithm on (rooted) out-trees although in contrast we prove NP-completeness on directed acyclic graphs, as well as on instances with a constant number of nodes (and hence also constant treewidth). When we allow non-integer payments, we show by a linear programming argument that the problem Bailout Minimization can be solved in polynomial time.

Citation

Stewart, I., Kutner, D., Friedetzky, T., Trehan, A., & Mertzios, G. (2025). Payment Scheduling in the Interval Debt Model. Theoretical Computer Science, 1028, Article 115028. https://doi.org/10.1016/j.tcs.2024.115028

• Journal Article Type: Article
• Acceptance Date: Dec 6, 2024
• Online Publication Date: Dec 13, 2024
• Publication Date: Feb 28, 2025
• Deposit Date: Dec 10, 2024
• Publicly Available Date: Dec 17, 2024
• Journal: Theoretical Computer Science
• Print ISSN: 0304-3975
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 1028
• Article Number: 115028
• DOI: https://doi.org/10.1016/j.tcs.2024.115028
• Public URL: https://durham-repository.worktribe.com/output/3213372