Consider an asset price $\left(S_{t}ight)_{t \in \mathbb{R}_{+}}$given by the stochastic differential equation

$$
\begin{equation*}
d S_{t}=r S_{t} d t+\sigma S_{t} d B_{t} \tag{8.46}
\end{equation*}
$$

where $\left(B_{t}ight)_{t \in \mathbb{R}_{+}}$is a standard Brownian motion, with $r \in \mathbb{R}$ and $\sigma>0$.

a) Write down the solution $\left(S_{t}ight)_{t \in \mathbb{R}_{+}}$of Equation (8.46) in explicit form.

b) Show by a direct calculation that Corollary 8.3 is satisfied by $\left(S_{t}ight)_{t \in \mathbb{R}_{+}}$.