Consider the compound Poisson process (Y_{t}:=sum_{k=1}^{N_{t}} Z_{k}), where (left(N_{t} ight)_{t in mathbb{R}_{+}})is a standard Poisson process with

Consider the compound Poisson process \(Y_{t}:=\sum_{k=1}^{N_{t}} Z_{k}\), where \(\left(N_{t}\right)_{t \in \mathbb{R}_{+}}\)is a standard Poisson process with intensity \(\lambda>0\), and \(\left(Z_{k}\right)_{k \geqslant 1}\) is an i.i.d. sequence of \(\mathcal{N}(0,1)\) Gaussian random variables. Solve the stochastic differential equation

\[d S_{t}=r S_{t} d t+\eta S_{t^{-}} d Y_{t}\]

where \(\eta, r \in \mathbb{R}\).