yu<-0.1        #up move of the market
r<-0           #interest rate
yd<--0.1       #down move of the market
u<-1.2         #upper (sell) threshold
l<-0.9         #lower (buy) threshold
T<-100         #number of time periods
Y<-sample(c(1+yd,1+yu),T,replace=TRUE)# vector of multiplicative coefficients
S1<-c(1,cumprod(Y))                   # vector of prices (S1_0, S1_1,..., S1_T), T+1 elements.
counter<-0                            # 0 : k < sigma, 1: sigma <= k <tau, 2 : tau<= k
theta<-vector()                       # predictable strategy (theta_0=0, theta_1, ..., theta_T), T+1 elements theta[i+1]=theta_i
phi<-vector()                         # amount of cash in the bank at time t, (phi_0, phi_1,..., phi_T), T+1 elements phi[i+1]=phi_i
v<-vector()                           # portfolio value at time t
theta[1]<-0                           # theta_0
phi[1]<-0                             # phi_0
v[1]<-0

for (i in 1:length(Y)){
  if(counter == 0 & S1[i]<=l){
    theta[i+1]<-1
    phi[i+1]<--S1[i]
    v[i+1]<-v[i]
    counter<-counter+1
  }
  else if(counter == 1 & S1[i]<u){
    theta[i+1]<-1
    phi[i+1]<-phi[i]
    v[i+1]<-theta[i+1]*S1[i+1]+phi[i+1]
  }
  else if (counter==1 & S1[i]>= u){
    theta[i+1]<-0
    phi[i+1]<-phi[i]+S1[i]
    v[i+1]<-phi[i+1]
    counter<-counter+1
  }
  else{
    theta[i+1]<-0
    phi[i+1]<-phi[i]
    v[i+1]<-v[i]
  }
}
if(theta[T+1]==1){
  theta[T+1]<-0
  phi[T+1]<-phi[T]+S1[T]
}
print(S1)
print(theta)
print(phi)

t<-0:T
plot(t, S1, type = "l", xlim = c(0,T), ylim = c(-1,1.5))
lines(t, theta, type = "l", col = "red")
lines(t, phi, type = "l", col = "blue")
lines(t, v, type ="l", col = "green")