Steady states, stability and bifurcations in multi-asset market models - Roberto Dieci; Noemi Schmitt; Frank Westerhoff (Bamberg University, Bamberg Economic Research Group (BERG), 2018)
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.
Keywords: D84; G12; G41; 330; multi-asset markets; replicator dynamics; nonlinear maps; stability and bifurcation analysis