Problem 1. Consider a market S with two assets and three states of the world. At time t = 0 we have that 58 = 1, So = 2 and at time t = T we have that Sy = (1, 1, 1), S, = (2, 1, 1) (a) Show that the market is incomplete. (b) Show that the market has arbitrage opportunities. () Identify an arbitrage opportunity. (d) Modify S, in such a way that the new market remains incomplete but becomes arbitrage free