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Selecting the optimum portfolio using fuzzy compromise programming and sharpe's single index-model

Author:
Bilbao Terol, Amelia MaríaUniovi authority; Pérez Gladish, Blanca MaríaUniovi authority; Antomil Ibias, JoséUniovi authority
Subject:

Portfolio Selection; Sharpe’S Single-Index Model; Fuzzy Numbers; Value, Fuzziness and Ambiguity; Fuzzy Compromise Programming

Publication date:
2006
Editorial:

Elsevier

Publisher version:
http://dx.doi.org/10.1016/j.amc.2006.04.028
Citación:
Applied Mathematics and Computation, 182(1), P. 644-664 (2006); doi:10.1016/j.amc.2006.04.028
Descripción física:
644-664
Abstract:

Different approaches besides the traditional Markowitz’s model have been proposed in the literature to analyze portfolio selection problems. Among them, Compromise Programming (CP) is a suitable multiobjective programming technique which allows the handling of several objectives in those situations in which the existence of a high level of conflict between criteria does not permit the simultaneous optimization of all the considered objectives. When objectives and constraints are in an imprecise environment Fuzzy CP arises as a suitable solving method. Imprecision will be quantified by means of fuzzy numbers that represent the continuous possibility distributions for fuzzy parameters and hence place a constraint on the possible values the parameters may assume. In this paper a new Fuzzy Compromise Programming approach is proposed based on the obtaining of the minimum fuzzy distance to the fuzzy ideal solution of the portfolio selection problem. Once this fuzzy distance has been obtained the second step consists of finding a crisp decision vector, an optimal portfolio, implying a fuzzy distance to the ideal solution the more accurate as possible to the fuzzy minimum distance previously obtained.

Different approaches besides the traditional Markowitz’s model have been proposed in the literature to analyze portfolio selection problems. Among them, Compromise Programming (CP) is a suitable multiobjective programming technique which allows the handling of several objectives in those situations in which the existence of a high level of conflict between criteria does not permit the simultaneous optimization of all the considered objectives. When objectives and constraints are in an imprecise environment Fuzzy CP arises as a suitable solving method. Imprecision will be quantified by means of fuzzy numbers that represent the continuous possibility distributions for fuzzy parameters and hence place a constraint on the possible values the parameters may assume. In this paper a new Fuzzy Compromise Programming approach is proposed based on the obtaining of the minimum fuzzy distance to the fuzzy ideal solution of the portfolio selection problem. Once this fuzzy distance has been obtained the second step consists of finding a crisp decision vector, an optimal portfolio, implying a fuzzy distance to the ideal solution the more accurate as possible to the fuzzy minimum distance previously obtained.

URI:
http://www.sciencedirect.com/science/article/pii/S0096300306003742
http://hdl.handle.net/10651/7042
ISSN:
0096-3003
DOI:
10.1016/j.amc.2006.04.028
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