QUESTION 1 Decision Analysis

(a) Discuss how a utility function can be assessed. What is a standard gamble and how is it used in determining utility values?
(b) Alan Barnes invests primarily in the share market. Recently he has become concerned about the share market as a good investment. During the next year he must decide whether to invest $10,000 in the share market or in a government bond at an interest rate of 9%.
Alan expects the share market to be good, fair or bad, giving a return of 14%, 8% or 0% respectively on his money.
1.Develop a decision matrix showing the two possible strategies, the three states of the share market and the monetary gains or losses under the six possible action-state scenarios.
Answer the following questions. Each answer must be supported with appropriate calculations and/or a table of figures, and you must state for questions 2 to 5 which alternative would be selected.
2. Which alternative would an optimist choose?
3. Which alternative would a pessimist choose?
4. Which alternative is indicated by the criterion of regret?
5. Assuming probability of a good market = 0.4, a fair market = 0.4 and a bad market = 0.2, using expected monetary values what is the optimum action?
6. What is the expected value of perfect information?