Let us consider a model with dates \(t=0,1,2\) with four states of nature \(\left\{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}\right\}\) and the following information flow

\[
\begin{gathered}
\mathscr{F}_{0}=\left\{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}\right\}, \\
\mathscr{F}_{1}=\left\{\mathscr{F}_{1}^{1}=\left\{\omega_{1}, \omega_{2}\right\}, \mathscr{F}_{1}^{2}=\left\{\omega_{3}, \omega_{4}\right\}\right\}, \\
\mathscr{F}_{2}=\left\{\left\{\omega_{1}\right\},\left\{\omega_{2}\right\},\left\{\omega_{3}\right\},\left\{\omega_{4}\right\}\right\} .
\end{gathered}
\]

Two assets are traded in the market, with dividends at \(t=2\) given by \[D=\left[\begin{array}{ll}4 & 2 \\2 & 3 \\2 & 9 \\4 & 3 \end{array}\right]\]
the prices of the two assets are \((3,2)\) in \(\mathscr{F}_{1}^{1},(2,3)\) in \(\mathscr{F}_{1}^{2}\), and \((1.1,0.9)\) in \(\mathscr{F}_{0}\).
(i) Is the market dynamically complete?
(ii) Are there arbitrage opportunities in the market?
(iii) If it exists, compute a risk neutral probability measure.
(iv) Determine the no-arbitrage price at the initial date \(t=0\) of a European Call option written on the first asset with strike price \(K=3\) and maturity \(T=2\).