# A4.pdf - ACTSC 372 Assignment#4 Due Monday April 4th 2:00...

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Unformatted text preview: ACTSC 372 — Assignment #4 Due Monday April 4th — 2:00 pm in the drop boxes _—-——————_——_—_____— 1. Describe all utility functions with a (positive) constant coefﬁcient of relative risk aversion. 2. Assume your utility function is given by u(x) = 1n(x) , and assume your current wealth is \$400,000. a. How much would you pay to insure against a loss of \$100,000 with probability 0.1%? b. Now assume your current wealth is \$1 million. How much will you pay to insure against this same loss? c. Prove the following statement about a person with a logarithmic utility function: the amount of money (as a proportion of current wealth) a person is willing to pay to insure against a loss of 10% of current wealth with probability p is constant. What is the constant? 3. Suppose that when a decision maker is given the following two gambles, A and B she chooses A (i.e. she prefers gamble A to gamble B). 3 A: Win \$50 with certainty B: Win \$100 with probability 60%, and 0 with probability 40%. The same decision maker is then asked to choose between gambles C and D: C: Win \$50 with 40% probability and win 0 with probability 60% D: Win \$100 with 24% and 0 with probability 76%. This time she chooses D. Explain why the decision maker has violated at least one of the axioms we discussed in class. (HINT: Consider L(A,0,0.4) and L(B,0,0.4).) 4. Assume your utility function is given by u(x) = 1n(x), and assume your current wealth is \$1000. How much would you pay for an investment that pays \$100 or \$0 with equal probability? Would you pay more or less for this investment if your current wealth were to increase? Explain. ...
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