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(a) Use the Ito formula to nd the mean and the variance of ekW(t), where k is a constant and W(t) is a standard Brownian

(a) Use the Ito formula to nd the mean and the variance of ekW(t), where

k is a constant and W(t) is a standard Brownian motion.

(b) The price of a stock S(t) at time t (with drift uand volatility o ) satises the stochastic

dierential equation

dS(t) = uS(t)dt + oS(t)dW(t)

Find the stochastic dierential equation associated with the processes: 1)

1/S(t) ; 2) S^n(t).

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