Past exam of the mathematics course of the University of Cambridge / 2007 / ii / Paper 3 / 27J / iii / Solution

At the upper time-one node, both exercise and continuation values are zero. At the lower node, immediate exercise gives three while continuation gives $2/3$, so exercise is strictly better. At time zero immediate exercise gives zero, whereas continuing givesThus continue at time zero and exercise at time one after a down move; at the upper node, exercise or continued holding is immaterial. One initial replicating portfolio for these optimal stopping values is $\Delta =-1/6$, $B=4$, costing $3/2$ and producing zero at stock 30 and three at stock 12.