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Portfolio Selection Models with Technical AnalysisBased Fuzzy Birandom Variables
You LI Bo WANG Junzo WATADA
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E97D
No.1
pp.1121 Publication Date: 2014/01/01 Online ISSN: 17451361
DOI: 10.1587/transinf.E97.D.11 Print ISSN: 09168532 Type of Manuscript: PAPER Category: Fundamentals of Information Systems Keyword: portfolio selection, technical analysis, fuzzy birandom variable, ValueatRisk, fuzzy birandom simulation, particle swarm optimization,
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Summary:
Recently, fuzzy set theory has been widely employed in building portfolio selection models where uncertainty plays a role. In these models, future security returns are generally taken for fuzzy variables and mathematical models are then built to maximize the investment profit according to a given risk level or to minimize a risk level based on a fixed profit level. Based on existing works, this paper proposes a portfolio selection model based on fuzzy birandom variables. Two original contributions are provided by the study: First, the concept of technical analysis is combined with fuzzy set theory to use the security returns as fuzzy birandom variables. Second, the fuzzy birandom ValueatRisk (VaR) is used to build our model, which is called the fuzzy birandom VaRbased portfolio selection model (FBVaRPSM). The VaR can directly reflect the largest loss of a selected case at a given confidence level and it is more sensitive than other models and more acceptable for general investors than conventional risk measurements. To solve the FBVaRPSM, in some special cases when the security returns are taken for trapezoidal, triangular or Gaussian fuzzy birandom variables, several crisp equivalent models of the FBVaRPSM are derived, which can be handled by any linear programming solver. In general, the fuzzy birandom simulationbased particle swarm optimization algorithm (FBSPSO) is designed to find the approximate optimal solution. To illustrate the proposed model and the behavior of the FBSPSO, two numerical examples are introduced based on investors' different risk attitudes. Finally, we analyze the experimental results and provide a discussion of some existing approaches.

