A projected dynamical systems model of general financial equilibrium with stability analysis. (English) Zbl 0858.90020

Summary: We present a dynamic model of general financial equilibrium. The model assumes utility-maximizing sectors in the economy that take the prices of the financial instruments as given. The economy, in turn, determines prices of the instruments that balance the supplies and demands. The financial adjustment process is shown to satisfy a projected dynamical system. This methodology is then used to establish, under certain conditions on the utility functions, both the stability and the asymptotical stability of the equilibrium asset, liability, and price pattern. This approach unveils a dynamic approach to competitive equilibrium problems that have, heretofore, been studied, principally, in the static framework of finite-dimensional variational inequality theory.


91B62 Economic growth models
91B50 General equilibrium theory
91B52 Special types of economic equilibria
91G80 Financial applications of other theories
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[1] Dupuis, P.; Nagurney, A., Dynamical systems and variational inequalities, Annals of operations research, 44, 9-42, (1993) · Zbl 0785.93044
[2] Zhang, D.; Nagurney, A., On the stability of projected dynamical systems, Journal of optimization theory and applications, 85, 97-124, (1995) · Zbl 0837.93063
[3] Nagurney, A., Network economics: A variational inequality approach, (1993), Kluwer Academic Publishers Boston, MA · Zbl 0873.90015
[4] Nagurney, A., Variational inequalities in the analysis and computation of general financial equilibrium, Journal of economic dynamics and control, 85, 161-184, (1994) · Zbl 0788.90011
[5] Smale, S., Dynamics in general equilibrium theory, American economic review, 66, 288-294, (1976)
[6] Smale, S., A convergence process of price adjustment and global Newton methods, Journal of mathematical economics, 3, 107-120, (1976) · Zbl 0354.90018
[7] Markowitz, H.M., Portfolio selection, The journal of finance, 77-91, (1952)
[8] Markowitz, H.M., Portfolio selection: efficient diversification of investments, (1959), John Wiley New York
[9] Sharpe, W.F., Portfolio theory and capital markets, (1970), McGraw-Hill New York
[10] Dong, J., General financial equilibrium with policy interventions: A variational inequality approach, Annals of operations research, 44, 227-241, (1993) · Zbl 0782.90007
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