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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 non-negative. 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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