I have trouble understanding Girsanov's theorem. The Radon Nikodym process Z is defined by:
Z(t)=exp(−∫t0ϕ(u)dW(u)−∫t0ϕ2(u)2du)
Now ˆP is a new probability measure. The trouble is I am not understanding how to go from old P to the new one. The old P is normally distributed with mean 0 and variance t. Now say I want to know the new probability for an infinitesimally small interval around 0.2. For that I need to know the value of Z at this interval (event you may say). And then I can multiply (integrate) the value of Z with old P, and get new ˆP.
Assume t is fixed.
I have no idea how to calculate the value of Z for this interval/event. Help would be appreciated.
No comments:
Post a Comment