# Why is L an interesting random time for a Brownian motion?

Let $$B$$ be a Brownian motion and define $$L=\sup \{ t \leq 1 : B_t = 0 \}$$.

My question is:

Why is $$L$$ an interesting random time?

Durrett's probability book proves something about the distribution of $$L$$ and also defines an analogous random variable and proves similar results for discrete simple random walks. But why do we care about this? When is $$L$$ useful? Why do I care about the last time I hit zero before $$t=1$$?