= Solution
At each time-2 node, replicate one positive put payoff using $\Delta$ shares and a current cash deposit $b$. Its two terminal values must satisfy $\Delta S_u+Rb=P_u$ and $\Delta S_d+Rb=P_d$, with $R=1.04$. Thus
$$
\Delta=\frac{P_u-P_d}{S_u-S_d},\qquad b=\frac{P_u-\Delta S_u}{1.04}.
$$
For the three nodes the hedge is
$$
\boxed{\begin{array}{c|c|c|c}
S_2&\Delta&b&P_2=\Delta S_2+b\\\hline
121&0&0&0\\
99&-21/22&103.95/1.04=99.95192&5.45192\\
81&-1&108/1.04=103.84615&22.84615
\end{array}}
$$
At $S_2=121$, both child puts expire worthless. At $99$, the child payoffs are $0$ and $18.9$; at $81$, they are $18.9$ and $35.1$. Substituting the hedge holdings into both child states verifies those payoffs exactly.
The writer is short the option and therefore \b[holds this positive replicating portfolio] to offset the liability. At the lower nodes that means shorting shares and depositing the proceeds together with the option value, rather than buying positive-delta stock. Rebalancing the replicating holdings along the tree is self-financing in the ideal model; the combined short option plus hedge has zero terminal liability in either child state.
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