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Unformatted text preview: MS&amp;E 211 Fall 2011 Linear and Nonlinear Optimization Nov 12, 2011 Prof. Yinyu Ye Assignment 5: Due 6:00 pm Tuesday, Nov. 29th Please write your solutions neatly  hard to read solutions will be penalized! Problem 1: Portfolio Management Problem Consider a portfolio management problem with two stocks. The expected mean and variance of the return on each share of stock A are 1 and 2, re spectively. The expected mean and variance of the return on each share of stock B are 2 and 3, respectively. The covariance of the return on one share each of the two stocks is 1. Your minimal expected return is = 1.2. You have $1 and you need to divide your investment between these two assets to minimize the portfolio variance. a) Suppose the allocation to each asset must be nonnegative. Write down the KKT conditions and find a solution. b) Now suppose negative allocations are possible. However, there is a restriction that your long position in stock B cannot exceed 0.5. In addition, your new minimal expected return is = 1.8. Write down the KKT conditions. Problem 2: Fishers Exchange Market Consider Fishers Exchange Market problem with two consumers and two goods. Consumer 1 has a budget ofconsumers and two goods....
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This note was uploaded on 01/16/2012 for the course MS&E 211 at Stanford.
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