Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 29K / d / Solution

For the American put option, compare exercise with continuation at time one. At $S_1=6$, both values are zero. At $S_1=4$, immediate exercise pays $1$, whereas the continuation value is the European value $4/9$, so exercise is optimal. At time zero, immediate exercise pays zero and continuation isThe optimal policy is therefore to continue at time zero, exercise at time one if $S_1=4$, and otherwise continue to maturity. This nodewise maximum is the Snell envelope value.

Solved by gpt-5.6-sol high.