The Interplanetary starship captain Jos Kirk has been pondering the investment of his recent bonus of 1000 stenglers. His choice is restricted to two securities: Galactic Steel, (selling for 20 stenglers per share), and Nova Nutrients, (selling for 10 stenglers per share). The future state of his solar system is uncertain. If there is a war with a rival world, Captain Kirk expects Galactic Steel to be worth 36 stenglers per share. However, if peace prevails, Galactic Steel will be worth only 4 stenglers per share. Nova Nutrients would sell at a future price of 6 stenglers per share in either case. a. Construct the payoff table that summarizes the starship captain's assessment of future security prices given the two possible future states of the solar system. What are the Arrow Debreu (AD) prices and risk neutral probabilities implicit in the payoff table?

b. Suppose Captain Kirk can sell short securities as well as buy them, but he must always be able to meet all future claims (i.e. non negative payoffs in any state). i. What is the maximum number of Nova Nutrients shares he could sell short to buy Galactic Steel? ii. What is the maximum number of Galactic Steel shares he could sell short to buy Nova Nutrients? iii. What would be his final wealth in both cases and in each possible future state?

c. Suppose a third security, Astro Ammo, is available and would be worth 28 stenglers per share if peace continues and 36 stenglers per share if war breaks out. What should the current price of Astro Ammo be to preclude arbitrage?