Is there a optional stopping theorem for backwards martingales ?
When $T$ is a non-positive and bounded stopping time then what kind of random variable is the following,
$\{X_{-T\wedge n}\}_{n\le-1}\tag1$
Is there a typo ? It doesn't make sense to me because $n$ is negative and $-T$ becomes positive ?
I should actually show if $\{X_k\}_k$ is a backward martingale with respect to backward filtration then so is $(1)$