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Seem4480 - Decision Methodology & Applications: Assignment 2

This document outlines an assignment for a decision methodology course. It provides instructions for submitting the assignment, grading details, and 4 questions to answer. Students must submit their responses by September 27th at 5:30pm to the assignment collection box, and the TA grading it is Mr. Yang, Chaolin. The 4 questions cover topics like risk attitudes, insurance premium calculations, expected utility analysis, and risk preferences for gambles based on a person's utility function.

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456 views2 pages

Seem4480 - Decision Methodology & Applications: Assignment 2

This document outlines an assignment for a decision methodology course. It provides instructions for submitting the assignment, grading details, and 4 questions to answer. Students must submit their responses by September 27th at 5:30pm to the assignment collection box, and the TA grading it is Mr. Yang, Chaolin. The 4 questions cover topics like risk attitudes, insurance premium calculations, expected utility analysis, and risk preferences for gambles based on a person's utility function.

Uploaded by

xieguagua
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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SEEM4480 - DECISION METHODOLOGY & APPLICATIONS

Fall 2013

Assignment 2
Due date: September 27, 2013, 5:30pm
Important notes:
1. You must submit your assignment on time. No late assignment will be accepted.
2. You must drop your assignment into the assignment collection box D08 @ 5/F of ERB. Please
dont hand in your assignment to the instructor or TAs.
3. Please include both your name and student ID in your submission.
4. Each question is worth 25 points.
5. TA Mr. Yang, Chaolin is responsible for grading this homework.
1. Mikes total wealth is $200,000, in which his house worth $150,000. Suppose his utility
function is u(x) = x (0.001 x)2 . There is 3% probability that his house would be destroyed
by fire and he will lose $150,000.
a(5pts) What is the risk attitude of Mike? What is the local degree of risk-aversion?
b(10pts) If he wants to buy a fire insurance, what is the maximum premium he would like
to pay? What is the minimum premium that the insurance company would charge?
c(10pts) Use w1 w2 plane to depict and illustrate your answers in part b. Explain your
figure.
2. St. Petersburg paradox. If a coin is tossed canonically until heads occurs, the probability that
i tosses will be required is (1/2)i . Now let l be the lottery which pays off $2i if i tosses are
required.
a(10pts) Show that a decision maker for whom EMV is a valid criterion of choice would be
happy to pay out his entire assets for the rights to this lottery.
b(10pts) Suppose a decision makers utility function can be described by the square root

function u(x) = x. How much would he be willing to pay for this lottery?
c(5pts) How much would you be willing to pay for this lottery?
3. A decision makers utility function can be described by the exponential function u(x) =
x
1 e R where R is his risk tolerance which is assessed to be $1210.
a(5pts) Find u($1000), u($800), u($0), and u($1250).
b(10pts) Find the expected utility for an investment that has the following payoff distribution:
P($1000)=0.33; P($800)=0.21; P($0)=0.33; P(-$1250)=0.13.
c(10pts) Find the certainty equivalent for the investment and the risk premium.
4. Suppose that a persons utility function for total wealth is
u(A) = 200A A2 ,

for 0 A 100

where A represents total wealth in thousands of dollars.

a(5pts) Graph this preference function. How would you classify this person with regard to
her attitude toward risk?
b(10pts) If the persons total assets are currently $10K, should she take a bet in which she
will win $10K with probability 0.6 and lose $10K with probability 0.4?
c(5pts) If the persons total assets are currently $90K, should she take the bet given in part
b?
d(5pts) Compare your answers to parts b and c. Does the persons betting behavior seem
reasonable to you? How could you intuitively explain such behavior?

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