Let
$$
D_t=\sum_{s=1}^t\frac{\delta_s}{N_s},
\qquad D_0=0,
$$
where the sum is componentwise, and set
$$
K_t=H_t+\eta_t(H_t\cdot D_{t-1}).
$$
Then
$$
X_t^{x,K}
=H_t\cdot(\delta_t+P_t)+N_tH_t\cdot D_{t-1}
=H_t\cdot\widetilde P_t
=\widetilde X_t^{x,H}.
$$
Also $K_{t+1}\cdot P_t=H_{t+1}\cdot\widetilde P_t$, so subtracting the new holdings value gives $C_t^{x,K}=\widetilde C_t^{x,H}$.


Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 211 / 1 / d / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-211/1/d/solution