= Solution
Write the <discount factor> as $D_t=B_t^{-1}=\exp(-\int_0^t r_sds)$. Splitting the time integral at $t$ gives
$$
\frac{P(t,T)}{B_t}
=\mathbb E^{\mathbb Q}[D_T\mid\mathcal F_t].
$$
The random variable $D_T$ lies in $(0,1]$ because the <short rate> is nonnegative and continuous on the finite maturity interval. A process of <conditional expectations> of an <integrable> terminal variable is a <martingale>, by the <tower property of conditional expectation>. Therefore
$$
\boxed{D_tP(t,T)\text{ is a bounded }\mathbb Q\text{-martingale}.}
$$
Back to article page
