ProblemSet4-2009 - Econ 6202, Fall 2009 Dmitry Shapiro...

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Econ 6202, Fall 2009 Dmitry Shapiro Problem Set 4 Due Tuesday October 6, 2009 1. An investor’s initial wealth is $ 30,000. The riskless asset has a rate of return equal to 1.05. The rate of return of the risky asset is 1.03 with probability 33 100 , and 1.06 with probability 67 100 . The von Neumann-Morgenstern utility function is u ( x ) = ln( x ). Find the amount of wealth that the investor puts into the risky asset. 2. An individual is seen to place an even-money $100,000 bet on the Lakers to win the NBA championship. If that individual has a ln( · ) von Neumann-Morgenstern utility function and his current wealth is $1,000,000, what is the minimum probability he must assign to the Lakers winning the championship? 3. An individual has wealth W . Her von Neumann-Morgenstern utility function over non-negative levels of wealth is u ( y ) = y ρ , where 0 < ρ < 1. The individual is offered the following bet. If she pays x , with probability 1/2 she receives nothing and with probability 1/2 she receives
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This note was uploaded on 10/20/2010 for the course ECON 6202 taught by Professor Shapiro during the Fall '09 term at UNC Charlotte.

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