"Technical Analysis in Financial Markets"

We define the vector variable

z_t=(P_1,t, P_2,t, P_3,t, MA_1,t, MA_2,t, MA_1,t, F_t^fund, F_t^ma)'.

In the following we denote the dynamical system by Φ, where

z_t=Φ(z_t-1).

Additive dynamic noise can be introduced into the system to obtain

z_t=Φ(z_t-1) + ε_t,

where ε_t=(ε_t, 0,0,0,0,0,0,0)' are iid random variables representing the model approximation error in that our model can only be an approximation of the real world. Because we assumed for all beliefs

V_t^h(r_t+1^P)=V_t^h

⎛
⎜
⎜
⎝

P_t+1+D_t+1-P_t

P_t

⎞
⎟
⎟
⎠

=σ²

and because P_t+1 and D_t+1 are independent, this implies

V_t^h(P_t+1)=P_t² σ² - V_t^h(D_t+1)=P_t² σ² - σ_δ².

Therefore, when we add dynamic noise to the deterministic skeleton, we draw ε_t iid from a normal distribution with expectation 0 and variance

σ_{ε_t}²=P_t² σ² - σ_δ².

6.4 Trading volume

In this section we describe a procedure to determine trading volume. The total number of short or long positions transferred from belief b to belief h at time t converges in probability to z_t-1^b q_t^h as the number of agents, each having zero market power, converges to infinity. The total number of long and short positions transferred to belief h from the other beliefs converges then in probability to

#long_t(→ h)

→

∑

b=1

z_t-1^b q_t^h I(z_t-1^b ≥ 0);

#short_t(→ h)

→

∑

b=1

z_t-1^b q_t^h I(z_t-1^b<0) |,

(40)

where I(.) is the indicator function. The demand for shares of each belief, under the equilibrium price which is set by the auctioneer, is equal to

z_t^h=

y_t^h W_t^h

P_t

→

y_t^h q_t^h W_t

P_t

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