The bounded local martingale $\pi$ is a true martingale. Its terminal condition is $\pi_T=U(T,v_T,S_T)=g(S_T)$, so
$$
\pi_0=\mathbb E[\pi_T]=\mathbb E[g(S_T)].
$$
This is also the <Feynman-Kac formula> for the displayed backward equation.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 211 / 3 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-211/3/b/solution