The discrete-time <fundamental theorem of asset pricing> supplies a strictly positive <martingale deflator> $Y$. Since the maturity-$T$ bond pays one unit at $T$, its deflated price is a martingale:
$$
Y_tP_t^T=\mathbb E(Y_T\mid\mathcal F_t).
$$
Division by $Y_t>0$ gives the formula.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 211 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-211/2/a/solution