Question 4 (a) Define the concept of a complete asset market. (b) Define an arbitrage opportunity. (c) Suppose that there are two dates (0 and 1), three assets, and three possible states of 4 mark:s 4 mark:s nature at date 1. Suppose that the three assets have the payoff matrix Z-3 6 9 6 9 15 where each column corresponds to a different asset. Asset 1 has price pi-4; asset 2 has price p2 -7; asset 3 has price p3 11 (i) Construct a portfolio comprising just assets 1 and 3 that replicates the payoff to 3 marks (ii) Find all state price vectors that are consistent with the asset prices. [7 marks (iii) Use your answer to (ii) to explain why this asset market is incomplete. [3 marks] iv) Use your answerto) to explain why this asset market contains no arbitrage the Arrow-Debreu security paying out in state 3 opportunities 4 mark:s Question 4 (a) Define the concept of a complete asset market. (b) Define an arbitrage opportunity. (c) Suppose that there are two dates (0 and 1), three assets, and three possible states of 4 mark:s 4 mark:s nature at date 1. Suppose that the three assets have the payoff matrix Z-3 6 9 6 9 15 where each column corresponds to a different asset. Asset 1 has price pi-4; asset 2 has price p2 -7; asset 3 has price p3 11 (i) Construct a portfolio comprising just assets 1 and 3 that replicates the payoff to 3 marks (ii) Find all state price vectors that are consistent with the asset prices. [7 marks (iii) Use your answer to (ii) to explain why this asset market is incomplete. [3 marks] iv) Use your answerto) to explain why this asset market contains no arbitrage the Arrow-Debreu security paying out in state 3 opportunities 4 mark:s