Solution
= Solution
For the bond maturing one period later,
$$
\mathbb E(Y_t\mid\mathcal F_{t-1})
=Y_{t-1}P_{t-1}^t
=\frac{Y_{t-1}}{1+r_t}.
$$
If $r_t\geq0$, this is at most $Y_{t-1}$, which is exactly the <supermartingale> property.
= Solution
For the bond maturing one period later,
$$
\mathbb E(Y_t\mid\mathcal F_{t-1})
=Y_{t-1}P_{t-1}^t
=\frac{Y_{t-1}}{1+r_t}.
$$
If $r_t\geq0$, this is at most $Y_{t-1}$, which is exactly the <supermartingale> property.