Question: Let S(t) be a positive stochastic process that satisfies the generalized geo- metric Brownian motion differential equation dS(t)-a(t)S(t)dt + (t)S(t)dW'(t) where a(t) and (t) are

Let S(t) be a positive stochastic process that satisfies the generalized geo- metric Brownian motion differential equation

dS(t)-a(t)S(t)dt + (t)S(t)dW'(t)

where a(t) and (t) are processes adapted to the filtration F(t), t associated with Brownian motion W(t), t 0, 20

a. Use It formula to compute d (log(S(t)) Simplify so that you have a formula for d (log(S(t)) that does not involve S(t).

b. Integration the formula in a. and then exponentiate to obtain the solution.

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