Multiple Objectives in Portfolio Selection

We begin this paper by first comparing the theory of present-day portfolio selection, which is a theory for standard investors (whose utility functions take on only the single argument of portfolio return), with a developing theory for non-standard investors (whose utility functions are allowed to take on additional arguments). Examples of additional arguments are dividends, liquidity, social responsibility, amount of short selling, and so forth. Then, with portfolio selection for non-standard investors taking on the form of a multi-objective stochastic programming problem, equivalent deterministic formulations involving more than mean and variance are explored. With the nondominated sets of nonstandard investors no longer frontiers, but now surfaces, the tools and techniques that must be imported from multiple criteria optimization to compute and analyze them are next discussed. The paper concludes with a list of research topics that are candidates for extending the multiple criteria portfolio selection material of this paper.