Question: Exercise . (Adapted from Bjrk ().) Define the process y = (yt) by yt = z t , where z = (zt) is a standard

Exercise . (Adapted from Björk ().) Define the process y = (yt) by yt =

z

t , where z = (zt) is a standard Brownian motion. Find the dynamics of y. Show that yt = 

t

z

s ds + 

t

z

s dzs.

Show that E[yt] ≡ E[z

t ] = t

, where E[ ] denotes the expectation given the information at time .

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