Solution
= Solution
On $\{H_T\ne0,X_{T-1}\leq0\}$,
$$
H_T\cdot(M_T-M_{T-1})
=X_T-X_{T-1}\geq-X_{T-1}\geq0.
$$
Dividing by $\|H_T\|$ proves $\xi\geq0$ there; outside that event $\xi=0$.
= Solution
On $\{H_T\ne0,X_{T-1}\leq0\}$,
$$
H_T\cdot(M_T-M_{T-1})
=X_T-X_{T-1}\geq-X_{T-1}\geq0.
$$
Dividing by $\|H_T\|$ proves $\xi\geq0$ there; outside that event $\xi=0$.