Correspondence: Francesc J. Ortí, Department Matemática Económica, Financiera y Actuarial, Universitat de Barcelona, Avda. Diagonal 696, Barcelona 8034, Spain. Tel: 34 93 403 4852; Fax: 34 93 403 4892; E-mail: forti@ub.edu

¹is a professor at the University of Barcelona (Spain) and collaborator professor at IEF (Institut d'Estudis Financers) on postgraduate courses. He graduated in Mathematics from the University of Barcelona and has a PhD in Business Administration and Direction from the University Rovira i Virgili (Spain), and is co-author of books and papers on Mathematical Business and Finances. His research interests include Finance, Portfolio Theory and Fuzzy Numbers and its applications.

²is a professor at the University of Barcelona (Spain) and collaborator professor at IEF (Institut d'Estudis Financers) on postgraduate courses. He graduated in Economics and Actuarial Studies from the University of Barcelona and PhD in Business Administration and Direction from the University of Barcelona (Spain). Moreover, he is the director of the Certified EFFAS Financial Analyst (CEFA) and the Certified International Investment Analyst (CIIA) programmes not only in Barcelona but also in Andorra. In addition, he is co-author of books and papers on Mathematical Business and Finance. He is a member of the Financial Analyst Institute of Spain (IEAF).

Received 25 February 2008; Revised 25 February 2008.

Abstract

Markowitz's classical model and other models derived from it have raised the portfolio problem using statistical instruments that assume a regular and efficient market. In this paper, the authors propose an alternative method using fuzzy numbers to represent the uncertainty of the future return on assets. Subsequently, we define measures for risk and for excess return on a portfolio. The resulting problem is a nonlinear multi-objective program with fuzzy parameters. Finally, we introduce one method to solve the resulting problem and an example.