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Nonlinear Dynamical Model of Regime Switching Between Conventions and Business Cycles

  • V. I. Yukalov
  • D. Sornette
  • E. P. Yukalova
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    We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes into account (i) the price formation delay between decision and investment by the second-order nature of the dynamical equations, (ii) the linear and nonlinear mean-reversal or their contrarian in the form of speculative price trading, (iii) market friction, (iv) uncertainty in the fundamental value which controls the amplitude of mispricing, (v) nonlinear speculative momentum effects and (vi) market regulations that may limit large mispricing drifts. We find markets with coexisting equilibrium, conventions and business cycles, which depend on (a) the relative strength of value-investing versus momentum-investing, (b) the level of uncertainty on the fundamental value and (c) the degree of market regulation. The stochastic dynamics is characterized by nonlinear geometric random walk-like processes with spontaneous regime shifts between different conventions or business cycles. This model provides a natural dynamical framework to model regime shifts between different market phases that may result from the interplay between the effects (i-vi).

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    File URL: http://arxiv.org/pdf/nlin/0701014
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    Paper provided by arXiv.org in its series Papers with number nlin/0701014.

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    Date of creation: Jan 2007
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    Publication status: Published in J. Econ. Behav. Org. 70 (2009) 206-230
    Handle: RePEc:arx:papers:nlin/0701014
    Contact details of provider: Web page: http://arxiv.org/

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    1. Bonomo, M. & Garcia, R., 1991. "Consumption and Equilibrium Asset Pricing: an Empirical Assessment," Cahiers de recherche 9126, Universite de Montreal, Departement de sciences economiques.
    2. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, vol. 80(3), pages 398-418, June.
    3. Marco Bonomo & René Garcia, 1994. "Disappointment Aversion as a Solution to the Equity Premium and the Risk-Free Rate Puzzles," CIRANO Working Papers 94s-14, CIRANO.
    4. J. Doyne Farmer, 1998. "Market Force, Ecology, and Evolution," Research in Economics 98-12-117e, Santa Fe Institute.
    5. Andersen, J.V. & Sornette, D., 2004. "Fearless versus fearful speculative financial bubbles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 565-585.
    6. Cecchetti, Stephen G. & Lam, Pok-sang & Mark, Nelson C., 1993. "The equity premium and the risk-free rate : Matching the moments," Journal of Monetary Economics, Elsevier, vol. 31(1), pages 21-45, February.
    7. Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
    8. Broekstra, Gerrit & Sornette, Didier & Zhou, Wei-Xing, 2005. "Bubble, critical zone and the crash of Royal Ahold," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(3), pages 529-560.
    9. Boyer, Robert & Orlean, Andre, 1992. "How Do Conventions Evolve?," Journal of Evolutionary Economics, Springer, vol. 2(3), pages 165-77, October.
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