Journal of Evolutionary Economics

, Volume 27, Issue 5, pp 1007–1040 | Cite as

An evolutive financial market model with animal spirits: imitation and endogenous beliefs

  • F. Cavalli
  • A. Naimzada
  • M. Pireddu
Regular Article


We propose a financial market model with optimistic and pessimistic fundamentalists who, respectively, overestimate and underestimate the true fundamental value due to ambiguity in the stock market. We assume that agents form their beliefs about the fundamental value through an imitative process, considering the relative ability shown by optimists and pessimists in guessing the realized stock price. We also introduce an endogenous switching mechanism, allowing agents to switch to the other group of speculators if they performed better in terms of relative profits. Moreover, the stock price is determined by a nonlinear mechanism. We study, via analytical and numerical tools, the stability of the unique steady state, its bifurcations and the emergence of complex behaviors, with possible multistability phenomena. To quantify the global propensity to optimism/pessimism of the market, we introduce an index, depending on pessimists’ and optimists’ beliefs and shares, thanks to which we are able to show that the occurrence of the waves of optimism and pessimism are due to the joint effect of imitation and switching mechanism. Finally, we perform a statistical analysis of a stochastically perturbed version of the model, which high lights fat tails and excess volatility in the returns distributions, as well as bubbles and crashes for stock prices, in agreement with the empirical literature.


Animal spirits Imitative process Evolutionary selection Financial markets Bifurcations Complex dynamics 

JEL Classification

B52 C62 D84 G02 



The authors thank Professor He and Professor Hommes for their valuable comments about the interpretation of the model and the consistency with real data, and all the participants to NED 2015 for helpful discussions.

The authors wish also to thank the anonymous Reviewers and Professor Dieci, Guest Editor of the Special Issue on “Nonlinear Economic Dynamics”, for the useful suggestions.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, Mathematical Finance and EconometricsCatholic University of Sacred HearthMilanoItaly
  2. 2.Department of Economics, Management and StatisticsUniversity of Milano-BicoccaMilanoItaly
  3. 3.Department of Mathematics and ApplicationsUniversity of Milano-BicoccaMilanoItaly

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