A class of linear interval programming problems and its application to portfolio selection

Lai, Kin Keung; Wang, Shouyang; Xu, Jiuping; Zhu, Shushang; Fang, Yong

doi:10.1109/tfuzz.2002.805902

Cited by 144 publications

(57 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Interval number represents a kind of uncertainty, and it has a great potential for application in different fields, such as establish fuzzy portfolio model and multi-objective portfolio model [37] [38]. An interval number is denoted as x  , which is defined as follows [37]. …”

Section: Interval Number Methodsmentioning

confidence: 99%

A Multi-Attribute Decision Making for Investment Decision Based on D Numbers Methods

Zuo¹,

Qin²,

Tian³

et al. 2016

APM

View full text Add to dashboard Cite

Investment decision is a traditional multi-attribute decision making (MADM) problem since it has many uncertainty factors and incomplete information such as investment value, cost, sales, etc. D numbers theory is a useful tool to deal with uncertainty factors and incomplete information. In this paper, interval number and D numbers theory are revealed in the uncertain factor and incomplete information of investment decision. The weights of uncertain factors are calculated using entropy weight method. Thus, a new MADM model for investment decision based on D numbers theory is proposed. Numerical example is used to illustrate the efficiency of the proposed method.

show abstract

Section: Interval Number Methodsmentioning

confidence: 99%

A Multi-Attribute Decision Making for Investment Decision Based on D Numbers Methods

Zuo¹,

Qin²,

Tian³

et al. 2016

APM

View full text Add to dashboard Cite

show abstract

“…(2000), the authors applied the possibility theory to cope with uncertainty and solve the portfolio optimization problem. According to Lai et al (2002), Wang and Zhu (2002), and Giove et al (2006) linear interval programming model has been used for portfolio selection. Carlsson et al (2002) introduced a possibilistic approach for selecting portfolios with the highest utility value assuming assets returns as trapezoidal fuzzy numbers.…”

Section: Literature Reviewmentioning

confidence: 99%

A fuzzy compromise programming approach for the Black-Litterman portfolio selection model

Gharakhani¹,

Sadjadi²

2013

dsl

View full text Add to dashboard Cite

In this paper, we examine advanced optimization approach for portfolio problem introduced by Black and Litterman to consider the shortcomings of Markowitz standard Mean-Variance optimization. Black and Litterman propose a new approach to estimate asset return. They present a way to incorporate the investor's views into asset pricing process. Since the investor's view about future asset return is always subjective and imprecise, we can represent it by using fuzzy numbers and the resulting model is multi-objective linear programming. Therefore, the proposed model is analyzed through fuzzy compromise programming approach using appropriate membership function. For this purpose, we introduce the fuzzy ideal solution concept based on investor preference and indifference relationships using canonical representation of proposed fuzzy numbers by means of their correspondingα-cuts. A real world numerical example is presented in which MSCI (Morgan Stanley Capital International Index) is chosen as the target index. The results are reported for a portfolio consisting of the six national indices. The performance of the proposed models is compared using several financial criteria.

show abstract

“…The upper bound of the objective value of the interval convex optimization problem (1)-(2) can be calculated from the two-level program of model (5)- (6). However, solving model (5)- (6) is not so straightforward because the outer program and inner program have different directions for optimization, i.e.…”

Section: Upper Boundmentioning

confidence: 99%

“…. [1,6] [0. According to model (9) -(10), the lower bound of objective value l Z can be formulated as: …”

Section: Upper Boundmentioning

confidence: 99%

Determining The Objective Value Range For A Class Of Interval Convex Optimization Problems

Borzabadi¹,

Heidarian²

2011

J. Math. Computer Sci.

View full text Add to dashboard Cite

This paper generalizes a method of determining the objective value range of quadratic programming problems to a general class of interval convex programming ones, where all coefficients in objective function and constraints are interval numbers. The upper bound and lower bound of the objective values of the interval quadratic program is calculated by formulating a pair of two-level mathematical programs. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into conventional one-level convex programming problem. Solving the pair of convex programs produces the interval of the objective values of the problem. Numerical results confirms the procedure of the presented approach.

show abstract

A class of linear interval programming problems and its application to portfolio selection

Cited by 144 publications

References 14 publications

A Multi-Attribute Decision Making for Investment Decision Based on D Numbers Methods

A Multi-Attribute Decision Making for Investment Decision Based on D Numbers Methods

A fuzzy compromise programming approach for the Black-Litterman portfolio selection model

Determining The Objective Value Range For A Class Of Interval Convex Optimization Problems

Contact Info

Product

Resources

About