How can i simulate N trajectories of a Geometric Brownian motion with an initial condition

Hi,

I'm a new user of Matlab. i have to simulate N trajectories of a Geometric Brownian motion with initial condition S1Begin > S1(optimal). S1Begin is the initial value, and S1optimal is the trigger value for undertaking investment. they are both input data.

my code is:

function [S, t] = geom_brownian( sigma, T, S1Begin, drift, dt, nb_traj)
% Geomteric Brownian Motion 
% uso:
%  S = geom_brownian( sigma, T, S0, mu, step)
% esempio:
%  [S, t] = geom_brownian( .12, 5, 50, 100, .05, 1/255);

nT = ceil(T/dt); % numero di passi = T/step
W  = sigma * sqrt(dt) * cumsum(randn(nT,nb_traj)); % W_k = sigma*sqrt(step)*(U_k + ... + U_0)
c  = repmat((drift - sigma^2/2) *dt * (1:nT)',1,nb_traj); 
S  = [repmat(S1Begin,1,nb_traj); S1Begin * exp( c + W)]; %S  = [repmat(S0,1,nb_traj); S0 * exp( c + W)];
if nargout > 1
   t = [0;dt * (1:nT)'];
end

and i don't know where to insert such a condition.

Thxx