5. Once again with T = 1 and S = 2, let the asset matrix be given by A= 1 T -1 -1 1 2 -1 -2 and suppose that all investors have the utility function u (c) = ln (CI) + In (C2) in particular, constant utility zero from present consumption. (1) Can you find an optimal portfolio for these investors? (2) Does there exist a strong arbitrage? Consider An Econor X m Course: 19-20 EC5320. Foundatix Problernst (5) pd. X Problems4 (5).pdf x + O File C/Users/Tricia/Downloads/Proble4%20(5).pdf 4. Again with T = 1 and S = 2, assume that there is only a single security with payoff z = (1,1)'. Suppose there is only one investor with utility function u(c) = Co + Ci + C2 and this investor can also consume negative amounts of each good. (1) Can you find an optimal portfolio for the investor? (2) Is there an arbitrage at a strictly positive price for the security? (3) If consumption were restricted to be nonnegative, what would be an optimal portfolio for the investor? > Problemst (5) pdf Problems4 (5) pdf x + 3: Consider An Econon x m Course: 19 20 EC5320 Foundati x File C:/Users/Tricia/Downloads/Problems4%20(5).pdf 1 State Prices 1. Draw a date-event tree for three future periods (T = 3), i.e. t = 0,1,2,3, and 15 states. How many immediate successor states does each state have? 2. Suppose in a finance economy with S = 2 and T = 1 there is only one asset which pays 1 GBP in each of the two possible future states. (1) Are markets complete or not? (2) In a diagram with the payoffs in the two states on the two axes, draw the asset span. 3. In a finance economy with T = 1 and S = 3 there are four securities, J = 4, with payoffs given by Z = 2 0 1 1 3 0 0 0 4 1 1 0 The prices of the AD securities are pi = 2, p = 1, and p = 3. (1) Are markets complete? (2) What are the prices of the four securities? (?) 5. Once again with T = 1 and S = 2, let the asset matrix be given by A= 1 T -1 -1 1 2 -1 -2 and suppose that all investors have the utility function u (c) = ln (CI) + In (C2) in particular, constant utility zero from present consumption. (1) Can you find an optimal portfolio for these investors? (2) Does there exist a strong arbitrage? Consider An Econor X m Course: 19-20 EC5320. Foundatix Problernst (5) pd. X Problems4 (5).pdf x + O File C/Users/Tricia/Downloads/Proble4%20(5).pdf 4. Again with T = 1 and S = 2, assume that there is only a single security with payoff z = (1,1)'. Suppose there is only one investor with utility function u(c) = Co + Ci + C2 and this investor can also consume negative amounts of each good. (1) Can you find an optimal portfolio for the investor? (2) Is there an arbitrage at a strictly positive price for the security? (3) If consumption were restricted to be nonnegative, what would be an optimal portfolio for the investor? > Problemst (5) pdf Problems4 (5) pdf x + 3: Consider An Econon x m Course: 19 20 EC5320 Foundati x File C:/Users/Tricia/Downloads/Problems4%20(5).pdf 1 State Prices 1. Draw a date-event tree for three future periods (T = 3), i.e. t = 0,1,2,3, and 15 states. How many immediate successor states does each state have? 2. Suppose in a finance economy with S = 2 and T = 1 there is only one asset which pays 1 GBP in each of the two possible future states. (1) Are markets complete or not? (2) In a diagram with the payoffs in the two states on the two axes, draw the asset span. 3. In a finance economy with T = 1 and S = 3 there are four securities, J = 4, with payoffs given by Z = 2 0 1 1 3 0 0 0 4 1 1 0 The prices of the AD securities are pi = 2, p = 1, and p = 3. (1) Are markets complete? (2) What are the prices of the four securities? (?)