Let $X_t$ be a solution to the SDE, $dX_t=X_t \,dt+X_t\,dW_t $, $X_0=x>0$ where $W_t$ is brownian motion, then the solution to this SDE is $X_t=xe^{\frac{t}{2}+W_t}$.
Let $\tau=\inf_{t>0} \{t:X_t\ge R\}$. I am not sure how to calculate the expectation of the stopping time $\mathbb{E}_x[\tau]$.
Thank you