{"title":"Portfolio optimization based on bi-objective linear programming","authors":"Marzie Izadi, Mohammad Ali Yaghoobi","doi":"10.1051/ro/2023170","DOIUrl":null,"url":null,"abstract":"In this study, we deal with a portfolio optimization problem including both risky and risk-free assets. We use the infinity norm criterion to measure portfolio risk and formulate the problem as a bi-objective linear optimization problem. Then, a single objective linear program is considered related to the bi-objective optimization problem. Using the well-known Karush-Kuhn-Tucker optimality conditions, we obtain analytic formula for an optimal solution. Moreover, we determine the whole efficient frontier by multi-criteria optimization techniques. Based on the theoretical results, two algorithms are proposed for finding the portfolio weights and the efficient frontier. Numerical examples are given for illustrating the new models and algorithms. Additionally, a simulation study has been conducted to assess the performance of the proposed method.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"26 3","pages":"0"},"PeriodicalIF":1.8000,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rairo-Operations Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/ro/2023170","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, we deal with a portfolio optimization problem including both risky and risk-free assets. We use the infinity norm criterion to measure portfolio risk and formulate the problem as a bi-objective linear optimization problem. Then, a single objective linear program is considered related to the bi-objective optimization problem. Using the well-known Karush-Kuhn-Tucker optimality conditions, we obtain analytic formula for an optimal solution. Moreover, we determine the whole efficient frontier by multi-criteria optimization techniques. Based on the theoretical results, two algorithms are proposed for finding the portfolio weights and the efficient frontier. Numerical examples are given for illustrating the new models and algorithms. Additionally, a simulation study has been conducted to assess the performance of the proposed method.
期刊介绍：
RAIRO-Operations Research is an international journal devoted to high-level pure and applied research on all aspects of operations research. All papers published in RAIRO-Operations Research are critically refereed according to international standards. Any paper will either be accepted (possibly with minor revisions) either submitted to another evaluation (after a major revision) or rejected. Every effort will be made by the Editorial Board to ensure a first answer concerning a submitted paper within three months, and a final decision in a period of time not exceeding six months.
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