Thanks for the references Paul, I will take a look at them, and enjoy them!

Hi Moreno,

                   You kind of give me an opportunity of publicising my research. But I think you can take a look at my paper on String Theoretic treatment of Financial Nanotechnology published in Journal of Physics D which creates Lagrangian Action barriers and Genetic Nanoscale Algorithms to deal with Brownian Motion in Stock Exchanges over time and space, on my RG page. I hope it helps your research. SKM

First,   I am going to assume you are interested in arithmetic

Brownian motion, in which case, the R code is:

#Generating Brownian motion trajectory

# Computational finance by Argimiro Arratia (2014) vol 1:, p148

library(base)

install.packages(R.utils)

library(R.utils)

install.packages("quantmod")

library(fbasics)

library(quantmod)

library(distrSim)

alpha = 0;

sigma=1;

T = 1;

n=2^(12);

x0=0.1;

########## generating a trajectory of arithmetic Brownian motion

dt = T/n

t = seq(from=0,to=T,by = dt);

x = c(x0, alpha*dt + sigma*sqrt(dt)*rnorm(n, mean=0, sd=1));

Xt = cumsum(x);

plot(t,Xt,type='l', xlab = "time")

#############################################################I

However, you might be more interested in Geometric Brownian motion, in which case the R code is as follows:

(Ibid, p. 152)

###For Geometric Brownian motion:

install.packages("sde")

library(sde)

mu = .16

sigma = .2

P0 = 40

T= 1/12 # 1 month

nt = 50

n = 2^(8)

dt = T/n

t = seq(from=0,to=T,by = dt)

X=matrix(rep(0,length(t)*nt), nrow= nt)

for (i in 1:nt) {X[i,]= GBM(x=P0, r=mu, sigma=sigma,T=T,N=n)}

## Plot

ymin=min(X)

ymax=max(X)

plot(t, X[1,], type='l', ylim=c(ymin,ymax), col=1, ylab="Price P(t)", xlab="time t")