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HW5_Soln - MS&E 252 Decision Analysis I Handout#15 Homework...

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MS&E 252 Handout #15 Decision Analysis I 11/4/2007 Page 1 of 15 HW #5 Solutions Homework Assignment #5 Solutions Students Distribution: 0 5 10 15 20 25 30 35 40 -INF-0 0-0.5 0.5-1 1-1.5 1.5-2 2-2.5 2.5-3 3-3.5 3.5-4 4-4.5 4.5-5 5-5.5 5.5-6 6-6.5 6.5-7 7-7.5 7.5-8 8-8.5 8.5-9 9-9.5 9.5-10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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MS&E 252 Handout #15 Decision Analysis I 11/4/2007 Page 2 of 15 HW #5 Solutions Score-by-Question Distributions: Score on HW Question (./1) -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 Question 1 10% 50% 90% Question 2 10% 50% 90% Question 3 10% 50% 90% Question 4 10% 50% 90% Question 5 10% 50% 90% Question 6 10% 50% 90% Question 7 10% 50% 90% Question 8 10% 50% 90% Question 9 10% 50% 90% Question 10 10% 50% 90%
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MS&E 252 Handout #15 Decision Analysis I 11/4/2007 Page 3 of 15 HW #5 Solutions Distinctions These distinctions were prepared by the teaching team and reflect our best belief of the meanings of these terms. Risk attitude : A person’s risk attitude is determined by the relationship between his or her certain equivalent of a monetary deal and the e-value of the monetary measure Risk neutral : certain equivalent for any monetary deal is the e-value of monetary measure. U-curve is linear. Risk averse : certain equivalent for any monetary deal is always <= e-value of monetary measure. U-curve is concave. Risk preferring : certain equivalent for any monetary deal is always >= e-value of monetary measure. U-curve is convex. Risk odds : r characterizes the risk attitude of a person who satisfies the delta property. Risk odds, r = p/(1-p), equals the odds of winning one monetary unit versus losing one monetary unit so that person is indifferent between accepting and rejecting the deal. p 1-p +1 -1 0 ~ Risk tolerance : 1/ln(r) where r is the risk odds as described above. Risk aversion : ln(r) where r is the risk odds as described above Delta property : A person satisfies the delta property if adding a constant amount b to all prospects of a deal increases the certain equivalent of that deal by b. For such a person, PISP and PIBP of a deal are the same. Also, his/her certain equivalent can be computed without considering the person’s current wealth. Value of Clairvoyance : The most decision maker D would be willing to pay (PIBP) for a clairvoyant’s services to eliminate uncertainties in a particular decision situation. Value of experiment = value of clairvoyance on result of experiment. Value with free clairvoyance : is the certain equivalent of a deal with clairvoyance on a given uncertainty, when the payment for clairvoyance on that uncertainty is $0.
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MS&E 252 Handout #15 Decision Analysis I 11/4/2007 Page 4 of 15 HW #5 Solutions Probabilistic questions 1) Solution: a Mishra buys the information from the computer. The certain equivalent of the bet decision without the machine is $2.00. Note that all prospects that stemming from a “Bet” decision branch are reduced by the $10 bet amount and that Mishra is indifferent about for whom to bet.
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