Consider a risky asset valued \(S_{0}=\$ 4\) at time \(t=0\), and taking only two possible values \(S_{1} \in\{\$ 2, \$ 5\}\) at time \(t=1\). Find the portfolio allocation \((\xi, \eta)\) hedging the claim payoff 

at time \(t=1\), compute its price \(V_{0}=\xi S_{0}+\$ \eta\) at time \(t=0\), and determine the corresponding risk-neutral probability measure \(\mathbb{P}^{*}\).

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C = $0 if S = $5 $6 if S $2