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

The pair $(v_t,Y_t)$ is a Markov diffusion with infinitesimal generatorPart d shows that the terminal condition in the equation for $\tilde{U}$ is exactlywhen evaluated at $(v_T,Y_T)$. The Feynman-Kac formula applied to the displayed backward equation therefore givesPart c identifies the right side with ${\pi }_0$.