[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 e) Find the range of arbitrage prices for Y using the class M of all martingale measures for the model M. (f) Suppose that you have sold the claim Y for the price of 3 units of cash. Show that you may find a portfolio (x,) with the initial wealth x=3 such that V1(x,)>Y, that is, V1(x,)(i)>Y(i) for i=1,2,3 [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 e) Find the range of arbitrage prices for Y using the class M of all martingale measures for the model M. (f) Suppose that you have sold the claim Y for the price of 3 units of cash. Show that you may find a portfolio (x,) with the initial wealth x=3 such that V1(x,)>Y, that is, V1(x,)(i)>Y(i) for i=1,2,3