International Journal of Business and Economics Research
Volume 9, Issue 2, April 2020, Pages: 83-93
Received: Feb. 21, 2020;
Accepted: Mar. 5, 2020;
Published: Mar. 10, 2020
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Vladimir Kulipanov, Department of Control and Applied Mathematics, Moscow Institute of Physics and Technology, Moscow, Russian Federation
The last two decades of the XX century marked the starting point for the central banks across the globe to move their payment and settlement systems into Real Time Gross Settlement (RTGS) mode. Despite the fact that RTGS systems can effectively eliminate the credit exposure between the paying bank and the receiving bank at the interbank level by means of fast final and irrevocable money transfer, there is another serious problem associated with these systems. RTGS systems turned out to be liquidity-demanding arrangements, as opposed to deferred net settlement systems. Thus, the efficiency of liquidity management arrangements is the precondition of smooth RTGS operation, especially in tough times when liquidity is a systemic shortage. If liquidity management is inefficient, the RTGS system may stop operating properly by terminating in the grid-lock state brining chaos to the national economy. In this research we suggest the practical approach to solve the problem of seeking the maximization of aggregate value of payment instructions under liquidity shortage, including the most severe scenarios. The classification of the RTGS queue statuses is suggested and discussed. Some complementary results are articulated, including: (a) the statement that the formal mathematical optimization problem lies in the NP class of the computational complexity (the class of problems solved in polynomial time by nondeterministic Turing machine); (b) the equivalence between MaxFlow-MinCost problem (from the network flow theory) and the dual linear problem of the linear program relaxation of the initial optimization problem; (c) the illustration that no optimization strategy, other than the suggested one, can deliver substantially better optimization results. Despite enormous efforts, there were no previous research results reasonably claiming the near optimality of liquidity optimization strategy in RTGS systems under severe liquidity shortages. The results of this research may help the central banks and other RTGS system operators to ensure the protection of their payment systems from future liquidity crises and bring the resilience of respective national economies to the next level of sustainability.
The Gridlock-Proof Functionality in Real Time Gross Settlement Systems, International Journal of Business and Economics Research.
Vol. 9, No. 2,
2020, pp. 83-93.
Copyright © 2020 Authors retain the copyright of this article.
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Rivandra K. Ahuja, Thomas L. Magnanti, James B. Orlin “Network Flows: Theory, Algorithms, and Applications”.
Ford, L.R.; Fulkerson, D.R. (1956). "Maximal flow through a network". Canadian Journal of Mathematics. 8: 399 404. doi: 10.4153/CJM-1956-045-5
Thomas Cormen, Charles Leiserson, Roland Rivest “Introduction to Algorithms”, p. 536-573.
Christofides N., Graph theory: an algorithmic approach. 1975, London: Academic Press ISBN 0121743500 (ISBN 13: 9780121743505).
Michael M. Güntzer, Dieter Jungnickel, Matthias Leclerc; Efficient algorithms for the clearing of interbank payments; European Journal of Operational Research 106 (1998) p. 212-219.
Marco Galbiati Kimmo Soramäki. “Liquidity-saving mechanisms and bank behavior” Bank of England Working Paper № 400, July 2010.
Harry Leinonen (ed.) “Simulation studies of liquidity needs, risks and efficiency in payment networks”. Proceedings from the Bank of Finland Payment and Settlement System Seminars 2005–2006.
David Karger. Massachusetts Institute of Technology. Advanced Algorithms. Lecture 16: 10/11/2006. Minimum cost maximum flow, Minimum cost circulation, Cost/Capacity scaling.
A. V. Goldberg and R. E. Tarjan. Finding minimum-cost circulations by canceling negative cycles. J. Assoc. Comput. Mach., 36 (4): 873-886, 1989.
´E. Tardos. A strongly polynomial minimum cost circulation algorithm. Combinatorica, 5 (3): 247-255, 1985.
Shafransky Y. M., Doudkin A. A. An optimization algorithm for the clearing of interbank payments. European Journal of Operational Research, 2006, Vol. 171, 743-749.
Alexander Schrijver, Theory of Linear and Integer Programming. John Wiley & sons, 1998, ISBN 0-471-98232-6 (mathematical)
The simplex algorithm takes on average D steps for a cube. Borgwardt Karl-Heinz The simplex method: A probabilistic analysis. — Berlin: Springer-Verlag, 1987. — Vol. 1. — P. xii+268. — ISBN 3-540-17096-0.
Kantorovich L.V., Mathematical methods for production process planning and management // Leningrad State University Press, 1939 (in Russian language).
Gass Saul I., Linear Programming (Methods and Applications) Applied Science Department, International Business Machines Inc., Graduate School, U.S. Department of Agriculture, McGraw-Hill Book Company Inc., 1958.
Muravyov V.I., Method of regular improvement with the alternating-size basis for the linear programing. — Collection "Operational Research and Statistical Model Methods". — Leningrad: Leningrad State University Press, 1972 (in Russian language).
David Karger, 6.854 Advanced Algorithms, Minimum cost maximum flow, Minimum cost circulation, Cost/Capacity scaling, Lecture 16: 10/11/2006
E. Tardos. A strongly polynomial minimum cost circulation algorithm. Combinatorica, 5 (3): 247-255, 1985.