Abstract
In this paper, we consider two distinct classes of network problems – financial networks with intermediation and with electronic transactions and transportation network equilibrium problems, which have been modeled and studied independently. We then prove that the former problem can be reformulated as the latter problem through an appropriately constructed abstract network i.e., a supernetwork. The established equivalence allows one to then transfer the methodological tools, in particular, algorithms, that have been developed for transportation network equilibria to the financial network domain. In addition, this connection provides us with a novel interpretation of the financial network equilibrium conditions in terms of paths and path flows and a direct existence result. We further show how the theoretical results obtained in this paper can be exploited computationally through several numerical examples.
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References
Beckmann MJ, McGuire CB, Winsten CB (1956) Studies in the economics of transportation. Yale University Press, New Haven
Boyce DE, Mahmassani HS, Nagurney A (2005) A retrospective on Beckmann, McGuire, and Winsten’s Studies in the economics of transportation. Papers Reg Sci 84:85–103
Charnes A, Cooper WW (1967) Some network characterizations for mathematical programming and accounting approaches to planning and control. Account Rev 42:24–52
Dafermos S (1980) Traffic equilibrium and variational inequalities. Transportation Sci 14:42–54
Dafermos S, Nagurney A (1984) Stability and sensitivity analysis for the general network equilibrium – travel choice model. In: Volmuller J, Hamerslag R (eds) Proceedings of the ninth international symposium on transportation and traffic theory. Utrecht, The Netherlands, pp 217–232
Dafermos SC, Sparrow FT (1969) The traffic assignment problem for a general network. J Res Nat Bur Stand 73B:91–118
Dantzig GB, Madansky A (1961) On the solution of two-stage linear programs under uncertainty. In: Proceedings of the fourth berkeley symposium on mathematical statistics and probability, vol 1. University of California Press, Berkeley,
Dupuis P, Nagurney A (1993) Dynamical systems and variational inequalities. Ann Oper Res 44:9–42
Ferguson AR, Dantzig GB (1956) The allocation of aircraft to routes. Manage Sci 2:45–73
Florian M, Hearn D (1995) Network equilibrium models and algorithms. In: Ball MO, Magnanti TL, Monma CL, Nemhauser GL (eds) Network routing, handbooks in operations research and management science 8. Elsevier, Amsterdam, pp 485–440
Geunes J, Pardalos PM (2003) Network optimization in supply chain management and financial engineering: an annotated bibliography. Networks 42:66–84
Nagurney A (1993) Network economics: a variational inequality approach. Kluwer, Dordrecht
Nagurney A (2005) On the relationship between supply chain and transportation network equilibria: A supernetwork equivalence with computations. Transportation Res E (in press)
Nagurney A (2006) Supernetworks. In: Resende MGC, Pardalos PM (eds) Handbook of optimization in telecommunications. Springer Science and Business Media, New York, pp 1073–1119
Nagurney A, Cruz J (2003a) International financial networks with intermediation: modeling, analysis, and computations. Comput Manage Sci 1:31–58
Nagurney A, Cruz J (2003b) International financial networks with electronic transactions. In: Nagurney A (eds) Innovations in financial and economic networks. Edward Elgar Publishing, Cheltenham, pp 136–168
Nagurney A, Dong J (2002) Supernetworks: decision-making for the information Age. Edward Elgar Publishers, Cheltenham
Nagurney A, Dong J, Zhang D (2002) A supply chain network equilibrium model. Transportation Res E 38:281–303
Nagurney A, Ke K (2001) Financial networks with intermediation. Quant Finan 1:309–317
Nagurney A, Ke K (2003) Financial networks with electronic transactions: modelling, analysis, and computations. Quant Finan 3:71–87
Nagurney A, Siokos S (1997) Financial networks: statics and dynamics. Springer, Berlin Heidelberg New York
Nagurney A, Zhang D (1996) Projected dynamical systems and variational inequalities with applications. Kluwer, Boston
Nagurney A, Zhang D (1997) Projected dynamical systems in the formulation, stability analysis, and computation of fixed demand traffic network equilibria. Transportation Sci 31:147–158
Nash JF (1959) Equilibrium points in n-person games. Proc Nat Acad Sci USA 36:48–49
Nash JF (1951) Noncooperative games. Ann Math 54:286–298
Patriksson M (1994) The traffic assignment problem – Models and methods. VSP, Utrecht
Pardalos PM, Tsitsiringos NK (eds) (2002) Financial engineering, E-commerce and supply chain. Kluwer, Boston
Quesnay F (1758) Tableau economique, reproduced in facsimile with an introduction by Higgs H by the British Economic Society, 1895
Resende MGC, Pardalos PM (eds) (2006) Handbook of optimization in telecommunications. Springer Science and Business Media, New York
Rustem B, Howe M (2002) Algorithms for worst-case design and applications to risk management. Princeton University Press, Princeton
Storoy S, Thore S, Boyer M (1975) Equilibrium in linear capital market networks. J Finan 30:1197–1211
Thore S (1969) Credit networks. Econometrica 36:42–57
Thore S (1970) Programming a credit network under uncertainty. J Money Banking Finan 2:219–246
Thore S (1980) Programming the network of financial intermediation. Universitetsforslaget, Oslo Norway
Smith MJ (1979) Existence, uniqueness, and stability of traffic equilibria. Transportation Res 13B:259–304
Wardrop JG (1952) Some theoretical aspects of road traffic research. In: Proceedings of the Institute Civil Engineers, Part II, pp 325–378
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Liu, Z., Nagurney, A. Financial Networks with Intermediation and Transportation Network Equilibria: A Supernetwork Equivalence and Reinterpretation of the Equilibrium Conditions with Computations. CMS 4, 243–281 (2007). https://doi.org/10.1007/s10287-006-0010-3
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DOI: https://doi.org/10.1007/s10287-006-0010-3
Keywords
- Financial networks
- Transportation network equilibrium
- Variational inequalities
- Supernetworks
- Projected dynamical systems
- Computation of equilibria