Consider a discrete time one-period market model with three primary assets: two stocks S and U, as well as a savings account. The interest rate is zero. The stock prices are given by S0 = U0 = 10, S1 = and U1 = , where and are two independent random variables, each taking two possible values 5 and 15 with positive probabilities.

a) Find two distinct equivalent martingale measures (EMMs) for this model. (Note that the discounted price processes of all three primary assets must be martingales under each EMM.)

b) Find a contract, whose payoff depending on S1 and U1, that cannot be replicated by a trading portfolio in this market model

c) Suppose that and are no longer independent, but instead have the following joint distribution: P( = 5, = 5) = P( = 5, = 15) = P( = 15, = 15) = 1/3 . Prove that there is no EMM in this case.