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HO24-PS3-Solutions

HO24-PS3-Solutions - MS&E 352 Handout#23 Decision Analysis...

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MS&E 352 Handout #23 Decision Analysis II Mar 04, 2009 ______________________________________________________________________ ______________________________________________________________________ 03/07/06 Page 1 of 9 Problem Set #3 Problem Set #3 Solutions Grade Distribution 0% 5% 10% 15% 20% 25% 30% 35% 0-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70 71-75 76-80 81-85 86-90 91-95 96-100 Problem 1 – Discretization Practice [30 points] We designed this problem to give you practice in discretizing continuous distributions (here, a Gaussian or normal distribution), as well as to show you the accuracy of the different discretization methods. Willie Wafer, sole proprietor of Big Chip Little Chip Semi Conductors, faces an alternative whose net present value (NPV) has a normal distribution with mean of $0 and standard deviation of 1 million dollars. Willie follows the delta property and has a risk tolerance of 5 million dollars. You will find the cumulative distribution for Willie's alternative on the attached page (You can generate this for yourself using the NORMDIST function in Excel). You will compare the distributions and certain equivalents, which result from the different discretization methods.
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MS&E 352 Handout #23 Decision Analysis II Mar 04, 2009 ______________________________________________________________________ ______________________________________________________________________ 03/07/06 Page 2 of 9 Problem Set #3 Question 1: [20 points] Fill out the table on the following page. If you want partial credit, show your work on the moment-matching discretizations on a separate page. Answer: See table on next page. Error Codes: [1.1.1] – 2 to 5 points – At least one PISP calculation is wrong. [1.1.2] – 1 to 7 points – Mistake in or missing results for one of the two methods. [1.1.3] – 1 point – Minor mistake in the PISP calculations, such as: a) wrong sign; or b) because you did not exactly compute the probabilities of each degree (e.g. typed 0.33 instead of 1/3 for 3 degrees), your PISP’s are slightly off; or c) used a probability distribution for the equal areas method that did not make sense; d) rounded off all the answers, so it was impossible to compare accuracy; e) used incorrect risk tolerance
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MS&E 352 Handout #23 Decision Analysis II Mar 04, 2009 ______________________________________________________________________ ______________________________________________________________________ 03/07/06 Page 3 of 9 Problem Set #3 A closed form equation exists to find the certain equivalent of a normal distribution, given its mean and variance. ~ x x x = - 1 2 ( ρ where ~ x = certain equivalent x = mean ( x = variance ρ = risk tolerance As an aside, if you know the mean and variance of your distribution (even a non-normal distribution), this equation can serve as an approximation to the certain equivalent of that distribution.
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