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

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## 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.

## Keywords

Multi-asset markets Replicator dynamics Nonlinear maps Stability and bifurcation analysis## JEL Classification

D84 G12 G41## References

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