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Unformatted text preview: enough to determine whether B second order stochastically dominates A. Additional remark (for those who are confused about this question; you didn’t need to write this): In Lecture 6, when we went over first and second order stochastic dominance, we saw that second order stochastic dominance (which is defined as the lottery being preferred by any concave utility function) is the same as a mean preserving spread (slide 34). Then, on slides 40
42, we saw that some lotteries with the same mean and higher variance are preferred by some (reasonable) concave utility functions. Therefore, checking the variance is not enough to verify second order stochastic dominance. (Checking the variance only, for lotteries with the same mean, is the same as checking only for quadratic utility functions – since those are utility functions leading to the mean
variance criterion).
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Part II: Quantitative Question Question 8. (28 minutes) Peter owns a house evaluated at $750,000. He also owns a total of $250,000 in other assets. Peter believes that a major earthquake, which would severely destroy the property and reduce its value to $240,000, will happen with probability 2%. Peter's total wealth is equal to the value of his house plus the total amount of other assets. Peter has a Bernoulli utility function u(W ) = W , where W denotes his total wealth. ∂
1
∂2
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Hints: W=
, and . W =−
2
∂W
∂W
2W
4W W
€
a. (4 minutes) What is the Value at Risk of Peter’s total wealth at 4% level? €
€ 1 million. b. (4 minutes) What is the expected shortfall of Peter's total wealth at 4% level? 1, 000, 000 490, 000
+
= 745, 000 . 2
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c. (4 minutes) Is Peter's coefficient of absolute risk aversion increasing...
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This note was uploaded on 02/03/2014 for the course INSR 205 taught by Professor Kent/smetters/nini during the Spring '09 term at UPenn.
 Spring '09
 KENT/SMETTERS/NINI

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