### Abstract

This paper proposes an investor-friendly random fuzzy portfolio selection model considering both robustness and adjustment of future asset returns derived from investor’s forecasts for financial tendency using a fuzzy inference method. It is important to predict the price or the return of each asset appropriately considering current market trends in portfolio optimization. In this paper, a standard multi-factor model, namely Arbitrage Pricing Theory (APT), is introduced as an asset pricing model. In addition, in order to extend standard APT by integrating important rules of current markets trends derived from technical analysis and fundamental analysis, each factor of APT is assumed to be a random fuzzy variable whose mean is adjusted by the fuzzy reasoning method, particularly product–sum-gravity method. Furthermore, it is also important for the investor to reduce the worst case of the total loss in terms of risk-averse. Therefore, worst-case conditional Value-at-Risk, which is a robust programming approach without assuming some specific random distribution, is considered. Since the proposed model is formulated as a biobjective programming problem both minimizing the value of worst-case conditional Value-at-Risk and maximizing the total expected return, it is equivalently transformed into the deterministic nonlinear programming problem using the satisficing trade-off method, and the efficient algorithm to obtain the optimal portfolio is developed. By solving our proposed model, the investor can obtain the risk-averse optimal portfolio with the large total return complying with current market trends.

Original language | English |
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Pages (from-to) | 1-17 |

Number of pages | 17 |

Journal | Annals of Operations Research |

DOIs | |

Publication status | Accepted/In press - 2017 Mar 4 |

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### Keywords

- Efficient algorithm
- Fuzzy reasoning method
- Portfolio selection problem
- Random fuzzy programming
- Worst-case conditional Value-at-Risk

### ASJC Scopus subject areas

- Decision Sciences(all)
- Management Science and Operations Research

### Cite this

*Annals of Operations Research*, 1-17. https://doi.org/10.1007/s10479-017-2458-7