Developments in Multi-Attribute Portfolio Selection

In this paper we reconcile why it is possible that people in finance view conventional portfolio selection as a single criterion problem and people in multiple criteria optimization view it as a bi-criterion problem. We then show how, for more complex investors, the theory of mean-variance portfolio selection can be extended to include additional objectives such as dividends, liquidity, turnover, number of securities in a portfolio, and so forth. This is followed by a discussion of the nature of the nondominated sets of multiple objective portfolio selection problems and developments underway for the solution of such problems.