Here is my question:
In our setups, the filtration satisfies the usual condition. $V$ is an increasing process with only jumps (between the jumps it is flat). We also know that $V$ is right continuous and previsible. Now, define a stopping time: $$\tau:= \inf\{t> 0|V_t\neq V_{t-}\}.$$ My question is whether $\tau$ is a previsible stopping time, i.e. there exists a sequence of stopping time $\tau_n$ such that $\tau_n<\tau$ and $\tau_n\uparrow \tau$. Thanks !