Consider an economy with two traded assets and three possible states of the world (i.e., \(N=2\) and \(S=3\) ), with price-dividend couple

\[D=\left[\begin{array}{ll}1 & 5 \\4 & 2 \\3 & 1\end{array}\right] \quad \text { and } \quad p=\left(\begin{array}{l}2.45 \\2.35\end{array}\right)\]

(i) Characterize the set of possible state prices.
(ii) Determine the space of attainable payoffs.
(iii) Verify that the arbitrage free price of any attainable payoff does not depend on the specific state price vector chosen.
(iv) Determine the interval of arbitrage free prices for the payoff \(c=(2,1,3)^{\top}\).
(v) Consider a Call option with strike price 2 written on the second security. Does the introduction of such a derivative make the market complete?