How to implement a Correlated Brownian Motion correctly

I have trouble implementing a Correlated Brownian Motion. I need the simulation for 1000 paths and T=5. Only the values of the evolution for t=1 and T=5 are relevant. The following code is running, but does not return the expected values. Does anybody know what I did wrong? Thankful for any advice or hint!

X1=100;
X2=90;
r=0.03;
sigma1=0.25;
sigma2=0.25;
rho=0.5;
T=5;

sigma=[sigma1 0;0 sigma2];
corr=[1 rho;rho 1];
cov=sigma*corr*sigma;

R=chol(cov,'lower');

N=1000;

X1_t=zeros(N,T+1);
X1_t(:,1)=A_0;
X2_t=zeros(N,T+1);
X2_t(:,1)=L_0;

dt=1;

for i=1:N   
    X=randn(T,2);
    W=X*R;
    for j=2:T+1
    X1_t(i,j)=X1_t(i,j-1)*exp(r*dt+sigma1.*W(j-1,1)-(sigma1.^2./2)*dt);
    X2_t(i,j)=X2_t(i,j-1)*exp(r*dt+sigma2.*W(j-1,2)-(sigma2.^2./2)*dt);   
    end  
end

[Walter Roberson]

Please do not close Questions that have an Answer.

[Walter Roberson]

Do not close questions that have an answer. The answer may be of use to other people.

Answer 1

[jean claude]

here is a clear demonstration http://www.goddardconsulting.ca/matlab-monte-carlo-assetpaths-corr.html

[Nina]

Thank you very much for the link, but I would like to solve it with the for-loops :-/