A <T-forward measure> is a probability measure $Q^T$, equivalent to the physical measure, under which prices expressed in units of the positive maturity-$T$ bond are martingales. Equivalently, every attainable payoff $X_T$ has time-$t$ price
$$
\pi_t=B_t^T\mathbb E_{Q^T}[X_T\mid\mathcal F_t].
$$
The zero-coupon bond is the <numéraire>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 211 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-211/2/a/solution