Portfolio optimization in real financial markets with both uncertainty and randomness

Abstract

Financial market is a complex system full of unknown and indeterminacy. It is well known that uncertainty and randomness are two basic types of indeterminacy. Hence, the complexity of real financial markets may lead to various types of security returns. They are usually assumed as random variables when there are enough historical data. If there is a lack of available data, they can be considered as uncertain variables. However, uncertainty and randomness often exist simultaneously. In this paper, we consider a portfolio optimization problem in real financial markets with both uncertainty and randomness. First, the skewnesses for three kinds of uncertain random variables are derived. Then, in an uncertain random environment, considering different risk preferences, a mean-variance-skewness model for the portfolio optimization problem is proposed. In addition, we use the normalization method to eliminate the impact of investment returns and risks of different units. Finally, numerical simulations are carried out to show that the proposed model is realistic and applicable.