A model of cycles and bubbles under heterogeneous beliefs in financial markets

Figures & data

Figure 1. Euphoric scenario with stable and attractive spiral and parameters $r=0.01,\alpha =3,\beta =0.001,N=2,\mu =0.1,\lambda =0,c=0.$.

Figure 2. Euphoric scenario with unstable spiral and parameters$r=0.01,\alpha =2,\beta =0.005,N=2,\mu =0.1,\lambda =0.1,c=0$.

Figure 3. Euphoric scenario with unstable spiral yielding a limit cycle and parameters $r=0.01,\alpha =3,\beta =0.005,N=2,\mu =0.1,\lambda =0.11,c=0$.

Figure 4. Euphoric scenario with stable and attractive spiral and parameters$r=0.01,\alpha =3,\beta =0.007,N=2,\mu =2,\lambda =0.5,c=-0.5$.

Figure 5. Euphoric scenario with stable and attractive node and parameters $r=0.01,\alpha =2,\beta =0.01,N=2,\mu =6,\lambda =0.2,c=-0.5$.

Figure 6. Euphoric scenario with stable and attractive node and parameters$r=0.01,\alpha =2,\beta =0.005,N=2,\mu =-0.5,\lambda =0.1,c=0.1$.

Figure 7. Cautious scenario with saddle and stable and attractive node and parameters$r=0.01,\alpha =3,\beta =0.005,N=2,\mu =2,\lambda =-0.1,c=0$.

Figure 8. Cautious scenario with saddle and parameters$r=0.01,\alpha =3,\beta =0.005,N=2,\mu =-0.1,\lambda =-0.1,c=0.2$.

Figure 9. Cautious scenario with two stable nodes and parameters$r=0.01,\alpha =2,\beta =0.005,N=2,\mu =2,\lambda =-0.1,c=-0.04$.

Figure 10. Euphoric scenario with higher return and parameters$r=0.08,\alpha =3,\beta =0.01,N=2,\mu =0.1,\lambda =0.1,c=0$.

Figure 11. Cautious scenario with higher return and parameters$r=0.08,\alpha =3,\beta =0.01,N=2,\mu =-1,\lambda =-0.1,c=0.1$.

Figure 12. Euphoric scenario with higher return and parameters$r=0.08,\alpha =3,\beta =0.005,N=2,\mu =0.1,\lambda =0.11,c=0$.

Figure 13. Cautious scenario with higher return and parameters$r=0.08,\alpha =3,\beta =0.005,N=2,\mu =-0.1,\lambda =-0.1,c=0.2$.

Table 1. Summary of the different types of equilibria that are found in the two scenarios (see Theorem 3.1 and Theorem 3.2)

		euphoric scenario(λ>0)	cautious scenario(λ<0)
${\tilde{\epsilon }}_i$	$\mu <1$	stable and attractive spiral unstable spiral unstable spiral with limit cycle	saddle
	$\mu >1$	stable spiral stable and attractive node	stable and attractive node saddle
${\epsilon }_{\bar{r}}$	$\mu <0$	stable and attractive node saddle	stable and attractive node saddle
	$\mu >1$	saddle	stable and attractive nodesaddle
${\epsilon }_c$		unstable node saddle	stable and attractive node unstable node

Data availability statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.