# Hedging strategy for American Option

Good day,

I was asked to devise a hedging strategy for an American Option given the following claims.

Note, $$r=0$$ and the underlying stock pays a dividend of $$1$$ at time $$t=1.5$$

$$\begin{array}{|c|c|c|c|} \hline & S(t=0,\omega) & S(t=1,\omega)^* & S(t=2,\omega)^* \\ \hline \omega_1 & 6& 9& 11\\ \hline \omega_2 & 6& 9& 7\\ \hline \omega_3 & 6& 4& 7\\ \hline \omega_4 & 6& 4& 1\\ \hline \end{array}$$

I found this question which seems identical except this person did not use dynamic programming to find the value of the option at each node.

I found the same risk neutral probabilities but I found the values at the nodes to be as follows

$$V_{amer}(0)=\dfrac{8}{5}, V_{amer}(1,\{ \omega_1,\omega_2\})=3, V_{amer}(1,\{ \omega_3,\omega_4\})=\dfrac{2}{3}$$ $$V_{amer}(1,\{ \omega_1\})=6, V_{amer}(1,\{ \omega_2\})=2, V_{amer}(1,\{ \omega_3\})=2, V_{amer}(1,\{ \omega_4\})=0$$

The comment on this (Constructing a hedging strategy for an American option) post says its how much stock we need to short against the option at each node but Im not quite sure how that makes a hedging strategy.