Nondominated sets and surfaces in multiple criteria optimization and portfolio selection theory in finance

by 1970- Qi, Yue

Because of the degree to which the effectiveness 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 effect 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 efficient (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. Index words: Multiple criteria decision making, Multiple criteria optimization, Portfolio selection, Efficient frontier, Nondominated surface Nondominated Sets and Surfaces in Multiple Criteria Optimization and Portfolio Selection Theory in Finance by Yue Qi B.S., Nankai University China, 1992 M.Eco., Nankai University China, 1996 A Dissertation Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Athens, Georgia 2004 c? 2004 Yue Qi All Rights Reserved Nondominated Sets and Surfaces in Multiple Criteria Optimization and Portfolio Selection Theory in Finance by Yue Qi Approved: Major Professor: Committee: Ralph E. Steuer K. Roscoe Davis Chris T. Stivers Elliot C. Gootman Qing Zhang Electronic Version Approved: Maureen Grasso Dean of the Graduate School The University of Georgia December 2004