A random-fuzzy portfolio selection DEA model using value-at-risk and conditional value-at-risk
- PDF / 685,693 Bytes
- 20 Pages / 595.276 x 790.866 pts Page_size
- 48 Downloads / 169 Views
(0123456789().,-volV)(0123456789(). ,- volV)
METHODOLOGIES AND APPLICATION
A random-fuzzy portfolio selection DEA model using value-at-risk and conditional value-at-risk Rashed Khanjani Shiraz1 • Madjid Tavana2,3
•
Hirofumi Fukuyama4
Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The complexity involved in portfolio selection has resulted in the development of a large number of methods to support ambiguous financial decision making. We consider portfolio selection problems where returns from investment securities are random variables with fuzzy information and propose a data envelopment analysis model for portfolio selection with downside risk criteria associated with value-at-risk (V@R) and conditional value-at-risk (CV@R). Both V@R and CV@R criteria are used to define possibility, necessity, and credibility measures, which are formulated as stochastic nonlinear programming programs with random-fuzzy variables. Our constructed stochastic nonlinear programs for analyzing portfolio selection are transformed into deterministic nonlinear programs. Moreover, we show an enumeration algorithm can solve the model without any mathematical programs. Finally, we demonstrate the applicability of the proposed framework and the efficacy of the procedures with a numerical example. Keywords Value-at-risk Conditional value-at-risk Portfolio selection Possibility measure Necessity measure Credibility measure Random-fuzzy variable
1 Introduction Financial decision making often involves semi-structured and unstructured situations characterized by fuzzy and random events. The purpose of this paper is four-fold. First, Communicated by V. Loia. & Madjid Tavana [email protected] http://tavana.us/ Rashed Khanjani Shiraz [email protected] Hirofumi Fukuyama [email protected] 1
School of Mathematics Science, University of Tabriz, Tabriz, Iran
2
Business Systems and Analytics Department, Distinguished Chair of Business Analytics, La Salle University, Philadelphia, PA 19141, USA
3
Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, 33098 Paderborn, Germany
4
Department of Business Management, Faculty of Commerce, Fukuoka University, Fukuoka, Japan
we develop a portfolio selection model where returns from investment securities are random variables with fuzzy information. The portfolio model is developed based on the value-at-risk (V@R) and conditional value-at-risk (CV@R). Second, both V@R and CV@R criteria are used to define possibility, necessity, and credibility measures, which are formulated as stochastic nonlinear programming programs with random-fuzzy variables. Third, the developed stochastic nonlinear programs are transformed into deterministic nonlinear programs. Fourth, four data envelopment analysis (DEA) portfolio models are proposed based on the developed framework. In portfolio selection, a critical issue for the investors is to determine an optimal configuration of the investment portfolio. The mean–vari
Data Loading...
