{"title":"Modeling of linear uncertain portfolio selection with uncertain constraint and risk index","authors":"Weiwei Guo, Wei-Guo Zhang, Zaiwu Gong","doi":"10.1007/s10700-024-09429-7","DOIUrl":null,"url":null,"abstract":"<p>Since securities market is subject to a great deal of uncertainty and complexity, the return of securities cannot be accurately estimated by historical data. In this case, it must use experts’ knowledge and judgment. Therefore, we investigate portfolio selection problems in such uncertain environments. First, this paper regards the rate of return on security as an uncertain variable which obeys linear uncertainty distribution, and then provides the analytical expressions of the corresponding risk, return and risk index in the uncertain portfolio selection environment. Afterwards, we construct three types uncertain portfolio selection models with uncertain constraint, namely, the minimizing risk, the maximizing return and the maximizing belief degree. Meanwhile, in order to more intuitively reflect the investor’s sense of loss, three types uncertain portfolio selection models considering both uncertain constraint and risk index are also constructed. These models are transformed into corresponding deterministic models. Finally, through an example analysis, this paper obtains the portfolio selection strategies under different objectives, compares the results under different models, and analyzes the sensitivity of the parameters.</p>","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Optimization and Decision Making","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10700-024-09429-7","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Since securities market is subject to a great deal of uncertainty and complexity, the return of securities cannot be accurately estimated by historical data. In this case, it must use experts’ knowledge and judgment. Therefore, we investigate portfolio selection problems in such uncertain environments. First, this paper regards the rate of return on security as an uncertain variable which obeys linear uncertainty distribution, and then provides the analytical expressions of the corresponding risk, return and risk index in the uncertain portfolio selection environment. Afterwards, we construct three types uncertain portfolio selection models with uncertain constraint, namely, the minimizing risk, the maximizing return and the maximizing belief degree. Meanwhile, in order to more intuitively reflect the investor’s sense of loss, three types uncertain portfolio selection models considering both uncertain constraint and risk index are also constructed. These models are transformed into corresponding deterministic models. Finally, through an example analysis, this paper obtains the portfolio selection strategies under different objectives, compares the results under different models, and analyzes the sensitivity of the parameters.
期刊介绍:
The key objective of Fuzzy Optimization and Decision Making is to promote research and the development of fuzzy technology and soft-computing methodologies to enhance our ability to address complicated optimization and decision making problems involving non-probabilitic uncertainty.
The journal will cover all aspects of employing fuzzy technologies to see optimal solutions and assist in making the best possible decisions. It will provide a global forum for advancing the state-of-the-art theory and practice of fuzzy optimization and decision making in the presence of uncertainty. Any theoretical, empirical, and experimental work related to fuzzy modeling and associated mathematics, solution methods, and systems is welcome. The goal is to help foster the understanding, development, and practice of fuzzy technologies for solving economic, engineering, management, and societal problems. The journal will provide a forum for authors and readers in the fields of business, economics, engineering, mathematics, management science, operations research, and systems.