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Nonlinear effects in a discrete-time dynamic model of a stock market

Listed author(s):
  • Gian-Italo Bischi


    (Università di Urbino)

  • Vincenzo Valori


    (Dipartimento di Matematica per le Decisioni - Università degli Studi di Firenze)

The time evolution of prices and savings in a stock market is modeled by a discrete time nonlinear dynamical system. The model proposed has a unique and unstable steady-state, so that the time evolution is determined by the nonlinear effects acting out of the equilibrium. The nonlinearities strongly influence the kind of long-run dynamics of the system. In particular, the global geometric properties of the noninvertible map of the plane, whose iteration gives the evolution of the system, are important to understand the global bifurcations which change the qualitative properties of the asymptotic dynamics. Such global bifurcations are studied by geometric and numerical methods based on the theory of critical curves, a powerful tool for the characterization of the global dynamical properties of noninvertible mappings of the plane. The model unfolds more complex chaotic and unpredictable trajectories as a consequence of increasing agents' "speculative" or "capital gain realizing" attitudes. The global analysis indicates that, for some ranges of the parameter values, the system has several coexisting attractors, and it may not be robust with respect to exogenous shocks due to the complexity of the basin of attraction.

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Paper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Mathematical Economics with number 2000-01.

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Length: 34
Date of creation: Jan 2000
Publication status: Published in: Chaos Solitons & Fractal, Vol. 11, Issue 13, 2103-2121, October 2000.
Handle: RePEc:flo:wpaper:2000-01
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  1. Bischi, Gian-Italo & Stefanini, Luciano & Gardini, Laura, 1998. "Synchronization, intermittency and critical curves in a duopoly game," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(6), pages 559-585.
  2. Bischi, Gian Italo & Gardini, Laura & Kopel, Michael, 2000. "Analysis of global bifurcations in a market share attraction model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 855-879, June.
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