Optimal Dynamic Clearing for Interbank Payments

We investigate the optimal clearing policy for a financial payment system composed of a number of member banks and a central bank in a dynamic setting, when new payment obligations or debts between member banks are generated over time. The central bank clears the debts among members in the system in order to minimize the costs, including the setup cost of each clearing, the variable cost of clearing the net debts, and the liquidity cost of uncleared debts. We formulate the problem using dynamic programming via state space reduction that provides a tractable framework to analyze and compute the optimal policy. We characterize the structure of the optimal policy and show that it is optimal for the central bank either to clear all the debts in the system or not to clear at all in each period under mild conditions. This structure leads to efficient computation of the optimal clearing policy. We further characterize the optimal clearing frequency based upon the deterministic approximation for the debt process. We conduct a comprehensive case study based on the data acquired from our industry partner, Payments Canada, to demonstrate the performance of the policy and its feasibility in industrial-size problems. This paper was accepted by Chung Piaw Teo, optimization. Funding: S. Chen’s research was supported by the National Natural Science Foundation of China Grants 72101273, 72188101, 72101258, and 71991463, the Humanities and Social Science General Foundation of the Ministry of Education of China Grant 21YJC630008, and the Hunan Provincial Natural Science Foundation of China Grant 2022JJ40643. Support for O. Baron’s research on this paper was provided by a grant from the Natural Science and Engineering Research Council of Canada (NSERC). N. Chen’s research was supported by the NSERC Discovery Grant RGPIN-2020-04038. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.00380 .