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hw5 - contest has been designed so that Joe will not know...

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IEOR E4007, G. Iyengar Jul. 25th, 2011 Homework #5 Due : The solution will be posted two weeks. 1. Efficient frontier Consider the portfolio selection problem described in Exercise 8.8 – the last problem of the previous homework. Construct the efficient frontier for this problem assuming that there is no risk-free asset in the market. Compute r min and σ 2 min . 2. Exercise 13.7 from Optimization for Finance Show that you can still use dynamic programming if the objective were to be changed to E n summationdisplay j =1 u ( X j ) , where u ( x ) = x - λx 2 and X j is the random profit from option j . 3. Exercise 14.3 from Optimization for Finance 4. Target planning In a youth contest, Joe will shoot a total of ten shots at four different targets. The
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Unformatted text preview: contest has been designed so that Joe will not know whether or not he hits any target until after he has made all ten shots. He obtains 6 points if any shot hits target 1, 4 points for hitting target 2, 10 points for hitting target 3, and 7 points for hitting target 4. At each shot there is an 80% chance that he will miss target 1, a 60% chance of missing target 2, a 90% chance of missing target 3, and a 50% chance of missing target 4, given that he aims at the appropriate target. If Joe wants to maximize his expected number of points, how many shots should he aim at each target? 5. Exercise 16.2 from Optimization for Finance 1...
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