# Robust Portfolio Selection Model with Random Fuzzy Returns Based on Arbitrage Pricing Theory and Fuzzy Reasoning Method

• Takashi Hasuike
• Hideki Katagiri
• Hiroshi Tsuda
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 186)

## Abstract

This paper considers a robust-based random fuzzy mean-variance portfolio selection problem using a fuzzy reasoning method, particularly a single input type fuzzy reasoning method. Arbitrage Pricing Theory (APT) is introduced as a future return of each security, and each factor in APT is assumed to be a random fuzzy variable whose mean is derived from a fuzzy reasoning method. Furthermore, under interval inputs of fuzzy reasoning method, a robust programming approach is introduced in order to minimize the worst case of the total variance. The proposed model is equivalently transformed into the deterministic nonlinear programming problem, and so the solution steps to obtain the exact optimal portfolio are developed.

## Keywords

Portfolio selection problem Arbitrage pricing theory (APT) Random fuzzy programming Fuzzy reasoning method Robust programming Equivalent transformation Exact solution algorithm

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## Authors and Affiliations

• Takashi Hasuike
• 1
• Hideki Katagiri
• 2
• Hiroshi Tsuda
• 3
1. 1.Graduate School of Information Science and TechnologyOsaka UniversitySuitaJapan
2. 2.Graduate School of EngineeringHiroshima UniversityHigashi-HiroshimaJapan
3. 3.Department of Mathematical Sciences, Faculty of Science and EngineeringDoshisha UniversityKyotanabeJapan