Abstract
The study of financial systems out of equilibrium and the underlying dynamics is a topic as important as the study of the systems in equilibrium. Central to dynamical systems is the evaluation of the stability of a system in terms of the ability of the system to maintain or restore its equilibrium when acted upon by forces tending to displace it. In addition, the development of algorithms for the computation of solutions to dynamical systems is as relevant as the investigation of qualitative properties of such systems.
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References
Alber, Y. I., “On the Solution of Equations and Variational Inequalities with Maximal Monotone Operators,” Soviet Mathematics Doklady 20 (1979) 871–876.
Armijo, L., “Minimization of Functions Having Continuous Partial Derivatives,” Pacific Journal of Mathematics 16 (1966) 1–3.
Arrow, K. J., and Hurwicz, L., Studies in Resource Allocation Processes, Cambridge University Press, New York, New York, 1977.
Arrow, K. J., Hurwicz, L., and Uzawa, H., Studies in Linear and Nonlinear Programming, Stanford University Press, Stanford, California, 1958.
Bakusinskii, A. B., and Polyak, B. T., “On the Solution of Variational Inequalities,” Soviet Mathematics Doklady 15 (1974) 1705–1710.
Bertsekas, D. P., “On the Goldstein-Levitin-Polyak Gradient Projection Method,” IEEE Transactions on Automatic Control 21 (1976) 174–184.
Conte, S. D., and de Boor, C., Elementary Numerical Analysis: An Algorithmic Approach, third edition, McGraw-Hill, Inc., New York, New York, 1980.
Dong, J., Zhang, D., and Nagurney, A., “A Projected Dynamical Systems Model of General Financial Equilibrium with Stability Analysis,” Mathematical and Computer Modelling 24 (1996) 35–44.
Dupuis, P., and Nagurney, A., “Dynamical Systems and Variational Inequalities,” Annals of Operations Research 44 (1993) 9–42.
Flam, S. D., “On Finite Convergence and Constraint Identification of Subgradient Projection Methods,” Mathematical Programming 57 (1992) 427–437.
Fukushima, M., “A Relaxed Projection Method for Variational Inequalities,” Mathematical Programming 35 (1986) 58–70.
Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1971.
Goldstein, A. A., “Convex Programming in Hilbert Space,” Bulletin of the American Mathematical Society 70 (1964) 709–710.
Henrici, P., Discrete Variable Methods in Ordinary Differential Equations, John Wiley Si Sons, Inc., New York, New York, 1962.
Hirsch, M. W., and Smale, S., Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, Inc., New York, New York, 1974.
Lambert, J. D., Computational Methods in Ordinary Differential Equations, John Wiley & Sons, Inc., New York, New York, 1973.
LaSalle, J., and Lefschetz, S., Stability by Liapunov’s Direct Method with Applications, Academic Press, Inc., New York, New York, 1961.
Nagurney, A., Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, Boston, Massachusetts, 1993.
Nagurney, A, “Variational Inequalities in the Analysis and Computation of Multi-Sector, Multi-Instrument Financial Equilibria,” Journal of Economic Dynamics and Control 18 (1994) 161–184.
Nagurney, A., “Parallel Computation,” in Handbook of Computational Economics, vol. 1, pp. 331–400, H. M. Amman, D. A. Kendrick, and J. Rust, editors, Elsevier Science B. V., Amsterdam, The Netherlands, 1996.
Nagurney, A., Dupuis, P., and Zhang, D., “A Dynamical Systems Approach for Network Oligopolies and Variational Inequalities,” Annals of Regional Science 28 (1994) 26–283.
Nagurney, A., and Siokos, S., “Dynamics of International Financial Networks: Modeling, Stability Analysis, and Computation,” Networks and Knowledge in a Dynamic Economy, M. Beckmann, B. Johansson, F. Snickars, and R. Thord, editors, Springer-Verlag, Berlin, Germany, 1996, in press.
Nagurney, A., Takayama, T., and Zhang, D., “Massively Parallel Computation of Spatial Price Equilibrium Problems as Dynamical Systems,” Journal of Economic Dynamics and Control 18 (1995a) 3–37.
Nagurney, A., Takayama, T., and Zhang, D., “ Projected Dynamical Systems Modeling and Computation of Spatial Network Equilibria,” Networks 26 (1995b) 69–85.
Nagurney, A., and Zhang, D., “On the Stability of Spatial Price Equilibria Modeled as a Projected Dynamical System,” Journal of Economic Dynamics and Control 20 (1996a) 43–63.
Nagurney, A., and Zhang, D., “Projected Dynamical Systems in the Modeling, Stability Analysis, and Computation of Fixed Demand Traffic Network Equilibria,” (1996b), to appear in Transportation Science.
Nagurney, A., and Zhang, D., Projected Dynamical Systems and Variational Inequalities with Applications, Kluwer Academic Publishers, Boston, Massachusetts, 1996c.
Okuguchi, K., and Szidarovszky, F., The Theory of Oligopoly with Multi-Product Firms, Lecture Notes in Economics and Mathematical Systems 342, Springer-Verlag, Berlin, Germany, 1990.
Perko, L., Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, Inc., New York, New York, 1974.
Zhang, D., and Nagurney, A., “On the Stability of Projected Dynamical Systems, Journal of Optimization Theory and Applications 85 (1995) 97–124.
Zhang, D., and Nagurney, A., “Stability Analysis of an Adjustment Process for Oligopolistic Market Equilibrium Modeled as a Projected Dynamical System,” Optimization 36 (1996a) 263–285.
Zhang, D., and Nagurney, A., “On the Local and Global Stability of a Travel Route Choice Adjustment Process,” Transportation Research 30B (1996b) 245–262.
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Nagurney, A., Siokos, S. (1997). Projected Dynamical Systems. In: Financial Networks. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59066-5_4
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DOI: https://doi.org/10.1007/978-3-642-59066-5_4
Publisher Name: Springer, Berlin, Heidelberg
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