Please answer this question clearly, thank you.

1. [12 marks] Single-period multi-state model. Consider a single-period market model M = (B, S) on a finite sample space 2 = {W, W2, W3}. We assume that the money market account B equals Bo = 1 and B1 = 4 and the stock price S = (S0, S1) satisfies So = 5 and Si = (36,20,4). The real-world probability Pis such that Pwi) = 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 for the contingent claim X = (5,1, -3) and com- pute the arbitrage price To(X) at time 0 through replication. (c) Compute the arbitrage price To(X) using the risk-neutral valuation formula with an arbitrary martingale measure Q from the class M. (d) Show directly that the contingent claim Y = (Y(W), Y (W2), Y (W3)) = (10,8,-2) is not attainable, that is, no replicating strategy for Y exists in M. (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 at time 0 the claim Y at the price of 3 units of cash. Show that you may find a portfolio (1,4) with the initial wealth r = 3 such that Vi(1,6) > Y, that is, V1(1,4) (wi) > Y(wi) for i = 1, 2, 3