A Risk-Free Protection Index Model for Portfolio Selection with Entropy Constraint under an Uncertainty Framework

Abstract

This paper aims to develop a risk-free protection index model for portfolio selection based on the uncertain theory. First, the returns of risk assets are assumed as uncertain variables and subject to reputable experts' evaluations. Second, under this assumption, combining with the risk-free interest rate we define a risk-free protection index (RFPI), which can measure the protection degree when the loss of risk assets happens. Third, note that the proportion entropy serves as a complementary means to reduce the risk by the preset diversification requirement. We put forward a risk-free protection index model with an entropy constraint under an uncertainty framework by applying the RFPI, Huang's risk index model (RIM), and mean-variance-entropy model (MVEM). Furthermore, to solve our portfolio model, an algorithm is given to estimate the uncertain expected return and standard deviation of different risk assets by applying the Delphi method. Finally, an example is provided to show that the risk-free protection index model performs better than the traditional MVEM and RIM.

Entropy and Semi-Entropies of LR Fuzzy Numbers’ Linear Function with Applications to Fuzzy Programming

“…Proof of Corollary 1. It follows from Definitions 6-8 and Equations (15), (24), and (27) immediately.…”

“…Example 5. Given that δ ∼ T (a, b, c) LR is a triangular fuzzy number in Example 1 and Figure 1a, on the basis of Equations (9) and (15), the entropy of δ can be deduced as:…”

“…Kosko [11] developed a general entropy measure based on an intuitive ratio of distances. Pal and Pal [12,13] introduced three types of entropy along with their applications to highlight their applicability to various problems (see also [14][15][16][17]).…”

Solving fully neutrosophic linear programming problem with application to stock portfolio selection

“…Portfolio selection (PS) problem is equivalent to the investor selecting the optimal portfolio from a set of possible portfolios Also, it focuses on the optimal allocation of one's wealth to obtain maximum profitable return under minimum risk control as discussed by Gao and Liu [13]. Markowitz [30] was the pioneer of the Modern Portfolio Theory.…”

“…Markowitz [30] was the pioneer of the Modern Portfolio Theory. Gao and Liu [13] based on the theory of uncertainty to develop a risk-free protection index model for PS. Liu and Qin [27] investigated a mean semi-absolute deviation model for uncertain.…”