Consider the single$-$period market model $M=(B,S^1,S^2,S^3)$ with four states of nature

$=\{{}_1,{}_2,{}_3,{}_4\}.$ Let the interest rate be $r=\frac{1}{9}.$ Stock prices at time $t=0$ are given by

$S_0^1=1,S_0^2=\frac{14}{9}$ and $S_0^3=\frac{8}{9}.$ Random stock prices at time $t=1$ are given by the following

table

Use FTAP to investigate whether this market model admits an arbitrage opportunity.

Is this market complete? Explain your answer.

The quality of your answer is very important for the mark. Please explain your answer

carefully, explain the notation you use, give clear references to definitions, theorems and

claims that you use to support your statements.