Int J Performability Eng ›› 2018, Vol. 14 ›› Issue (12): 3129-3139.

### A Risk-Free Protection Index Model for Multi-Objective Uncertain Portfolio Selection with Entropy and Variance Constraints

Jianwei Gaoa and Huicheng Liub*()

1. a Beijing Key Laboratory of New Energy and Low-Carbon Development, North China Electric Power University, Beijing, 102206,China
b School of Economics and Management, North China Electric Power University, Beijing,102206,China
•  Revised on  ; Accepted on
• Contact: Liu Huicheng E-mail:lhuicheng@ncepu.edu.cn

Abstract:

This paper discusses a multi-objective portfolio in the case where the distributions of security returns are subject to reputable experts' evaluations instead of historical data. Based on the assumption that the security returns of risk assets are uncertain variables, we put forward a new risk-free protection index (RFPI) model for multi-objective uncertain portfolio selections with entropy and variance constraints by using expected value as a measurement of portfolio return and take both variance and RFPI as measurements of a portfolio's risk measurements. To determine a suitable confidence level and criticality value of FRPI, we regard FRPI maximization as the second goal under the premise of maximum expected return rather than relying on the investors' risk preference and tolerance. To avoid excessive dispersion or concentration of investment, the proportion entropy and variance constraints are added to the FRPI model. The Delphi method is used to solve our model, and its algorithm is also shown. In the ending example, a comparative analysis is illustrated to show our multi-objective uncertain portfolio model with FRPI maximization added as the second objective function performs better than the traditional mean-variance model (MVM) and the risk-free protection index-entropy model (RFPIEM).