Nondominated sets and surfaces in multiple criteria optimization and portfolio selection theory in finance
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Because of the degree to which the e®ectiveness of an economy rests upon its ability to most carefully allocate its capital, and because of the degree to which the investment strategy of a portfolio manager or individual investor can e®ect the success of his or her organization or personal welfare, no stone should be left unturned in trying to better understand the investment process. In this dissertation, the view is taken that one of the reasons for complexity in the investment process is that criteria beyond variance and expected return often come into play, such as dividends, social responsibility, the number of securities in a portfolio, and so forth. One of the consequences of admitting criteria beyond the two is that the e±cient (nondominated) frontier becomes a nondominated surface, thus rendering much of traditional investment analysis a projection onto two dimensions of the often much more complicated problem of portfolio selection in higher dimensional space. In this dissertation, the types of nondominated surfaces that can result in multiple criteria optimization, particularly in multiple criteria portfolio optimization, are studied along with the development of methods for computing. Also, procedures are explored for locating the point on a given nondominated surface that represents the investor's multiple criteria optimal portfolio.