Let (S) be given by (10.4.2). Give the dynamics of (S^{k}). [begin{equation*} S_{t}=S_{0} exp left[left(b-phi lambda-frac{sigma^{2}}{2} ight)

Let \(S\) be given by (10.4.2). Give the dynamics of \(S^{k}\).

\[\begin{equation*}
S_{t}=S_{0} \exp \left[\left(b-\phi \lambda-\frac{\sigma^{2}}{2}\right) t+\sigma W_{t}+[\ln (1+\phi)] N_{t}\right]=S_{0} e^{X_{t}} \tag{10.4.2}
\end{equation*}\]