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Steady states, stability and bifurcations in multi-asset market models

Author

Listed:
  • Roberto Dieci

    (University of Bologna)

  • Noemi Schmitt

    (University of Bamberg)

  • Frank Westerhoff

    (University of Bamberg)

Abstract

We provide a full analytical treatment of a multi-asset market model in which speculators have the choice between two risky and one safe asset. As it turns out, the dynamics of our model is driven by a four-dimensional nonlinear map and may undergo a transcritical, flip or Neimark–Sacker bifurcation. While the first bifurcation is associated with an undervaluation of the risky assets, the latter two may trigger (complex) endogenous dynamics. To facilitate our analysis, we first study a simpler two-dimensional setup of our model in which speculators can only switch between one risky and one safe asset.

Suggested Citation

  • Roberto Dieci & Noemi Schmitt & Frank Westerhoff, 2018. "Steady states, stability and bifurcations in multi-asset market models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 357-378, November.
    • Handle: RePEc:spr:decfin:v:41:y:2018:i:2:d:10.1007_s10203-018-0214-3
    DOI: 10.1007/s10203-018-0214-3
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    Cited by:

    1. Christoph March & Marco Sahm, 2019. "The Perks of Being in the Smaller Team: Incentives in Overlapping Contests," CESifo Working Paper Series 7994, CESifo.
    2. Nivedita Mukherji, 2022. "Complex dynamics in the market for loans," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 83-99, June.
    3. Arata, Yoshiyuki & Mundt, Philipp, 2019. "Topology and formation of production input interlinkages: Evidence from Japanese microdata," BERG Working Paper Series 152, Bamberg University, Bamberg Economic Research Group.
    4. Mundt, Philipp & Oh, Ilfan, 2019. "Asymmetric competition, risk, and return distribution," BERG Working Paper Series 145, Bamberg University, Bamberg Economic Research Group.
    5. Mikhail Anufriev & Davide Radi & Fabio Tramontana, 2018. "Some reflections on past and future of nonlinear dynamics in economics and finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 91-118, November.
    6. Philipp Mundt & Simone Alfarano & Mishael Milaković, 2022. "Survival and the Ergodicity of Corporate Profitability," Management Science, INFORMS, vol. 68(5), pages 3726-3734, May.
    7. Proaño, Christian R. & Lojak, Benjamin, 2020. "Animal spirits, risk premia and monetary policy at the zero lower bound," Journal of Economic Behavior & Organization, Elsevier, vol. 171(C), pages 221-233.

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    More about this item

    Keywords

    Multi-asset markets; Replicator dynamics; Nonlinear maps; Stability and bifurcation analysis;
    All these keywords.

    JEL classification:

    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G41 - Financial Economics - - Behavioral Finance - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making in Financial Markets

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