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7 . ( a ) Jim is considering investing in a venture for which the returns are as follows. There are three exogenous states of
a Jim is considering investing in a venture for which the returns are as follows. There are three exogenous states of nature that mean that the investment will make either a good return s no return s or a large financial loss s: s s s Invest I Do not invest D i Determine the optimal action under each of the following decision rules: the extreme pessimist; the extreme optimist; and the Hurwicz Criterion with a pessimismoptimism index of ii At what value for would your decision change in part i Sketch this in a diagram and explain why the choice changes. iii Determine Jims best action under minimaxregret. b By referring to Jims problem above, consider whether the decision rules provide a good guide to decisionmaking under statecontingent uncertainty. c Now, suppose Jim has subjective beliefs about the probabilities with which the states of nature occur. What improvements can be made to form a better theory of choice under uncertainty using either the expected value or expected utility? Parts ab and c have equal weight
a Jim is considering investing in a venture for which the returns are as follows. There are three exogenous states of nature that mean that the investment will make either a good return s no return s or a large financial loss s:
s s s
Invest I
Do not invest D
i Determine the optimal action under each of the following decision rules: the extreme pessimist; the extreme optimist; and the Hurwicz Criterion with a pessimismoptimism index of
ii At what value for would your decision change in part i Sketch this in a diagram and explain why the choice changes.
iii Determine Jims best action under minimaxregret.
b By referring to Jims problem above, consider whether the decision rules provide a good guide to decisionmaking under statecontingent uncertainty.
c Now, suppose Jim has subjective beliefs about the probabilities with which the states of nature occur. What improvements can be made to form a better theory of choice under uncertainty using either the expected value or expected utility?
Parts ab and c have equal weight
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