Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 29L / d

Before the barrier has been hit, the two next-step continuation values areThe replicating stock holding on $(n-1,n]$ is thereforeThe bank holding is chosen from current wealth $U(n-1,s)$ as before. If the barrier has already been hit, the claim and both holdings are zero. Backward induction proves replication of the up-and-out payout.