Uncertain mean-CVaR model for portfolio selection with transaction cost and investors’ preferences

Abstract

Portfolio selection is a common practice among investors, scholars often rely on probability statistics to construct portfolios based on the Markowitz mean–variance model. However, due to the complexity of the stock market and the limitations of historical data, it may not be possible to fully predict the future market. In such situations, it is necessary to incorporate expert knowledge and judgments to obtain estimates of security return rates. This paper proposes a class of portfolio models suitable for uncertain environments. We employ the uncertainty theory and Arbitrage Pricing Theory (APT) to measure tail risk and construct a new uncertain mean-Conditional Value-at-Risk (CVaR) model. Additionally, to better match investors’ preferences, this paper takes into account transaction costs and liquidity needs. To solve this problem, we design a hybrid algorithm that incorporates these factors. Finally, we present a numerical experiment to illustrate the performance of the proposed model. In summary, our study offers a novel approach to portfolio selection that considers uncertainty theory, tail risk, and investors’ preferences. The results demonstrate that the proposed uncertain mean-CVaR model with hybrid algorithm optimization can improve portfolio performance in uncertain market conditions.