Hey valiant.
Are you given the rules for the Ito lemma to relate the integrals of the random and deterministic parts? (Once you have this then it becomes a match and fudge game).
Hi all,
Been trying to make sense of this for a couple days now, but my background in calculus is a little light.... Taking a financial engineering class and trying to work a solution for the following:
W_{t} is a Brownian motion. Use Ito's Lemma to derive dX = µ(W,t)dt + σ(W,t)dW_{t} for the following function:
X_{t }= exp{ ∫_{0}^{t} θdW_{s} – 1/2 ∫_{0}^{t} θ^{2}ds }
Thanks so much in advance!!
Val
No there should be a general version in terms of expressing X(t) as a function of two integrals: one with a Wiener component and the other with a deterministic component: both for general functions that modulate the dWt and the dt components of the the original dXt (which you have written there).
I can't remember it off hand since it is pretty complex.