A variable x starts at zero and follows the generalized Wiener process

dx = a dt + b dz
where time is measured in years. During the first two years a=3 and b=4 . During the following three years a=6 and b=3 .

What is the expected value of the variable at the end of 5 years
A. 16
B. 20
C. 24
D. 30

C
During the first two years, the drift per year is 3 and so the total drift is 3×2 or 6 . During the next three years, the drift per year is 6 and the total drift is 6×3 = 18 . The total drift over the five years is 6+18 =24 . Given that the variable starts at zero, its expected value at the end of the five years is therefore 24 .