Currently studying Ito's calculus. Looking on the GBM model: $ \frac{d S_t}{S_t} = μ dt + \sigma d B_t$ we end up on the expected stock price at time t: $E[S_t]=s_0 e^{\mu t}$.What does actually $\mu$ represents?
My initial thought is the opportunity cost of Capital for investements with the same characteristics (risk) and time horizon,that produces NPV=0.Also, $\mu$ is the instantenious expect return for dt $\rightarrow$ 0.
Finally, I wonder whether there is a Connection between GBM and martingale processes.