Title: Portfolio selection problems with normal mixture distributions including fuzziness

Authors: Takashi Hasuike, Hiroaki Ishii

Addresses: Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan. ' Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan

Abstract: In this paper, several portfolio selection problems with normal mixture distributions including fuzziness are proposed. Until now, many researchers have proposed portfolio models based on the stochastic approach, and there are some models considering both random and ambiguous conditions, particularly using fuzzy random or random fuzzy variables. However, the model including normal mixture distributions with fuzzy numbers has not been proposed yet. Our proposed problems are not well-defined problems due to randomness and fuzziness. Therefore, setting some criterions and introducing chance constraints, main problems are transformed into deterministic programming problems. Finally, we construct a solution method to obtain a global optimal solution of the problem.

Keywords: normal mixture distribution; fuzziness; uncertain programming; portfolio selection; portfolio models; fuzzy numbers; randomness.

DOI: 10.1504/IJKESDP.2010.035904

International Journal of Knowledge Engineering and Soft Data Paradigms, 2010 Vol.2 No.3, pp.207 - 223

Published online: 08 Oct 2010 *

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