# Tag Info

The first the solution to: $$dS_t = S_t\left[\mu dt +\sigma dW_t\right]$$ The second is the solution to: $$dS_t = S_t\left[\left(\mu -\frac{\sigma^2}{2}\right)dt + \sigma dW_t\right]$$ The difference is that the first one is a martingale when $\mu$ is equal to zero while the second one is not:  \mathbb{E}[S_0 exp(\sigma W_t)]= ...