Risk Neutral Pricing and Financial Mathematics: A Primer

b. 

$E\left[\ln \frac{S_{52}}{S_0}\right]=\left[\left(0.001-\frac{{0.02}^2}{2}\right)0.52\right]=0.0416$

$\mathrm{Var}\left[\ln \frac{S_{52}}{S_0}\right]={\sigma }^{2}T={0.02}^2\cdot 52=0.0208$

6.23. First, divide both sides of the differential by M−S_t to obtain:

$\frac{\mathrm{d}{S}_t}{M-S_t}=\mu \mathrm{d}t+\sigma \mathrm{d}{Z}_t$

Since the integral of dS_t/(M−S_t) for real-valued functions S_t equals −ln(M−S_t), we will use the expression ln(M−S_t) to obtain the correct solution for the stochastic process S_t