### 抄録

This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities and decision makers' predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a portfolio selection problem is provided to compare our proposed models with the basic model.

元の言語 | English |
---|---|

ページ（範囲） | 159-180 |

ページ数 | 22 |

ジャーナル | Central European Journal of Operations Research |

巻 | 17 |

発行部数 | 2 |

DOI | |

出版物ステータス | Published - 2009 6 |

外部発表 | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Management Science and Operations Research

### これを引用

**Probability maximization models for portfolio selection under ambiguity.** / Hasuike, Takashi; Ishii, Hiroaki.

研究成果: Article

*Central European Journal of Operations Research*, 巻. 17, 番号 2, pp. 159-180. https://doi.org/10.1007/s10100-008-0082-y

}

TY - JOUR

T1 - Probability maximization models for portfolio selection under ambiguity

AU - Hasuike, Takashi

AU - Ishii, Hiroaki

PY - 2009/6

Y1 - 2009/6

N2 - This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities and decision makers' predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a portfolio selection problem is provided to compare our proposed models with the basic model.

AB - This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities and decision makers' predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a portfolio selection problem is provided to compare our proposed models with the basic model.

KW - Multi-scenario model

KW - Portfolio selection problem

KW - Probability maximization model

KW - Stochastic programming

UR - http://www.scopus.com/inward/record.url?scp=67349255440&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349255440&partnerID=8YFLogxK

U2 - 10.1007/s10100-008-0082-y

DO - 10.1007/s10100-008-0082-y

M3 - Article

AN - SCOPUS:67349255440

VL - 17

SP - 159

EP - 180

JO - Central European Journal of Operations Research

JF - Central European Journal of Operations Research

SN - 1435-246X

IS - 2

ER -