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Let a(t) and B(t) be non-random time-dependent functions. X(0) = 1 and X(t) satisfies the following SDE dX(t) = a(t)X(t)dt + (t)X(t)dW (t) (a)

 

Let a(t) and B(t) be non-random time-dependent functions. X(0) = 1 and X(t) satisfies the following SDE dX(t) = a(t)X(t)dt + (t)X(t)dW (t) (a) (b) Solve X(t) Show that X(t) is lognormal and derive the mean and variance of In X(t).

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