The parameter γ controls for the maximum and minimum fraction of wealth the technical trader can invest in the risky asset. The parameter λ controls for the location of the extrema. Within some band around the moving average, which depends on the value of λ, ytMA increases (or decreases) to a maximum (or minimum) value γ (or -γ). Outside this band the further away price deviates from the moving average, the more ytMA decreases in absolute value.
Figure 6.2: Demand function exponential moving average belief
6.3.3 Market equilibrium
Wealth per agent, total wealth and market clearing
The number of shares agent
j who follows belief
h holds in the risky asset at time
t depends on his individual wealth and the equilibrium price, that is
Here
Wj,t is the wealth of agent
j at time
t, which depends on the fraction of the wealth invested at time
t-1, that is
|
|
| Wj,t= |
| ( |
1+rF+yj,t-1 (rtP-rF) |
) |
Wj,t-1= |
|
| |
⎛
⎜
⎜
⎝ |
1+rF+yj,t-1 |
⎛
⎜
⎜
⎝ |
|
-(1+rF) |
⎞
⎟
⎟
⎠ |
⎞
⎟
⎟
⎠ |
Wj,t-1= |
|
| |
| R Wj,t-1 + |
( |
Pt+Dt-R Pt-1 |
) |
|
|
= |
|
| |
| R Wj,t-1 + |
( |
Pt+Dt-R Pt-1 |
) |
zj,t-1. |
|
|
(28) |
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