[12 marks] Single-period multi-state model. Consider a single-period market model M=(B,S) on a finite sample space ={1,2,3}. We assume that the money market account B equals B0=1 and B1=4 and the stock price S=(S0,S1) satisfies S0=2.5 and S1=(18,10,2). The real-world probability P is such that P(i)=pi>0 for i=1,2,3. (a) Find the class M of all martingale measures for the model M. Is the market model M arbitrage-free? Is this market model complete? (b) Find the replicating strategy (00,01) for the contingent claim X=(5,1,3) and compute the arbitrage price 0(X) at time 0 through replication