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Math Help - Portfolio Optimisation

  1. #1
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    Oct 2009
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    Portfolio Optimisation

    I am basically using a Lagrange technique to optimise a portfolio of 5 assets, with conditions that the weights must add up to one, and a utility function. I can explain in more depth where these constraint scome from if it helps, but I think if you see the Maths thats all thats need to be solved really.
    How to use utility function log(x/ ym ) to obtain the optimal portfolio where m is a number (usually >1)

    Introduce Lagrange multiplier
    L = log(x ) m log(y ) - (wT l 1)
    Now x and y are vectors too, and I am ultimately trying to find w.

    Any ideas?
    I have attached a word document which explaines better.
    Attached Files Attached Files
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