If you wait long enough, almost surely. But while that’s a visible reason to dislike additive random walk models, I don’t think it’s the most compelling- the underlying step change in price dynamics does appear to be a percentage shift, not an additive shift. (If the negativity were the only issue, then you can just set up the random walk to be reflect at 0 so it always stays nonnegative.)
The point can be formulated even stronger: An additive random walk will go negative.
If you wait long enough, almost surely. But while that’s a visible reason to dislike additive random walk models, I don’t think it’s the most compelling- the underlying step change in price dynamics does appear to be a percentage shift, not an additive shift. (If the negativity were the only issue, then you can just set up the random walk to be reflect at 0 so it always stays nonnegative.)