A process is <predictable process>[previsible] when it is measurable with respect to the predictable sigma-algebra. The deterministic process $H_t=\mathbf1_{[1,\infty)}(t)$ is predictable because deterministic Borel processes are predictable, but it is not left-continuous at $t=1$ on any sample path.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 202 / 2 / a / Solution

 Solution (source code)