In the specific application of the model used in this paper, it is assumed that fundamentalists have the beliefs , and that trend chasers, who believe prices follow the process , , i.e. that prices are trending upward, have the corresponding belief that . Finally, it is assumed that dividends follow the first-order autoregressive process (18) Before proceeding, it may be helpful to summarize the main components of the model: Baseline asset pricing Dividends Asset pricing w/diff beliefs if , Share of agents of each type if Share of agents of each type Herding propensity Fundamentalist beliefs Trend-chasing beliefs This model has the fundamental solution: (19) When agents are allowed to switch between fundamental and trend-chasing beliefs, the solution is:
In the specific application of the model used in this paper, it is assumed that fundamentalists have the beliefs , and that trend chasers, who believe prices follow the process , , i.e. that prices are trending upward, have the corresponding belief that . Finally, it is assumed that dividends follow the first-order autoregressive process (18) Before proceeding, it may be helpful to summarize the main components of the model: Baseline asset pricing Dividends Asset pricing w/diff beliefs if , Share of agents of each type if Share of agents of each type Herding propensity Fundamentalist beliefs Trend-chasing beliefs This model has the fundamental solution: (19) When agents are allowed to switch between fundamental and trend-chasing beliefs, the solution is: