Consider a one-period, three-state economy with two assets traded. Asset 1 has a price of 0.9 and pays a dividend of 1 no matter what state is realized. Asset 2 has a price of 2 and pays 1, 2, and 4 in state 1, 2, and 3, respectively. The real-world probabilities of the states are 0.2, 0.6, and 0.2, respectively. Assume absence of arbitrage.

(a) Find the state-price vector ψ∗ and the associated state-price deflator. What portfolio generates a dividend of ψ∗?

(b) Find the state-price deflator ζ ∗ and the associated state-price vector. What portfolio generates a dividend of ζ ∗?

(c) Find a portfolio with dividends 4, 3, and 1 in states 1, 2, and 3, respectively. What is the price of the portfolio?