Geometric BM , SDE

napolean80 · April 26th, 2009, 9:39 pm

Solve the following differential equation.dX/X = mu*dt +sigma*dw. X(0) = x0. I am not getting the same answer for X =x exp((u-sigma^2)dt + W*sigma), which is the most common G. BM as everyone knows.

agerigk · April 27th, 2009, 10:09 am

I am not sure whether I understood your question but you are missing 1/2 it is(u-(sigma^2)/2)t

alphaquantum · April 27th, 2009, 11:43 am

find dln(X) by Ito. and yes, you missed 1/2.

napolean80 · April 27th, 2009, 11:51 am

QuoteOriginally posted by: alphaquantumfind dln(X) by Ito. and yes, you missed 1/2.I thought so too but the notes had a mistake then. thanks

daveangel · April 27th, 2009, 11:59 am

the 1/2 comes from the second derivative term in the Ito expansion which is also where you get the sigma^2 term

napolean80 · April 28th, 2009, 7:03 pm

yes got it! thanks.