Consider a financial market model with $d=1$ and $T=1.$ Writing $S$:$=S^1$ for the

discounted prices of the only risky asset, assume that $S_0=1$ and $S_{1}in\{0,1,10\}$

each of them with probability $\frac{1}{3}.$

$($a$)$ Does this model fulfil non$-$arbitrage $($NA$)?$

$($b$)$ Identify the set of equivalent martingale measures.

$($c$)$ Identify a non$-$replicable European option.