Towards Uncertain Portfolio Selection (Decision making theories under uncertainty and its applications : the extensions of mathematics for programming)

Abstract

Uncertain portfolio selection is a new branch of portfolio theory which is defined to be a methodology for selecting portfolio based on belief degree functions and uncertainty theory. When selecting portfolio, investors must first obtain the distribution functions of the candidate securities' returns. If the distribution functions are not believed to be close enough to the frequencies of the securities' future returns, the distribution functions have to be treated as bclicf degree functions which reflect humans' cstimations of the securities' future returns. In this case, uncertain portfolio selection should be adopted. Since in real life investors usually choose their portfolios from only those stocks whose companies' profits or other factors that affect faith in the companies change favourably and greatly, the stock returns cannot be reflected completely by historical return data and havc to bc given by investors' estimations. It is rarc that humans' estimations can be fairly close enough to the securities' future frequencies. Therefore, uncertain portfolio selection is a prospective research area and there is great room for research in this field. Generally speaking, what have bcen studied in traditional portfolio selection are worth researching on uncertain portfolio selection.