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Question: Consider an economy where there is uncertainty about the future. In particular, at the current date t all agents are unsure which of the 3 possible states (!1; !2; !3) will materi- alize at date t 1. There are two stocks in the economy. The Örst stock, A, is priced at time t with St = 10. At time t 1 it is expected to return a payo§X(!1) = 18 if state !1 realizes, X(!2) = 6 if state !2 realizes, and X(!3) = 12 if state !3 realizes. The second stock, B, has a price of 3 at date t. It is expected to return a payo§ of 4 in all three states of the world. The information about the two stocks is summarized in Table 1. 1. Show that there are no arbitrage opportunities in this economy. 2. Are state prices unique? Give example of two possible sets of state prices. Are markets complete in this case?
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