Consider the market given by the following matrix and price vector:

Y$=\left[\begin{array}{cc}10& 5\\ 20& 11\\ 15& 8\end{array}\right]=\left[\begin{array}{cc}14& 7\mathrm{.}5\end{array}\right]$

Verify that the vector of state prices $\left[\begin{array}{ccc}0\mathrm{.}4-0\mathrm{.}5& 0\mathrm{.}5-0\mathrm{.}5& \end{array}\right]$is compatible with No Arbitrage for somevalues of $$ and specify which values of $.$

$2.$Compute the minimum and maximum prices $($compatible with NA$)$ of the call and of the put option on the second asset with strike price $9$

$3.$ Suppose we introduce in the market a new asset with payos $[587]$ at the price $6.$ What is the resulting vector of state prices?