{"title":"满足准则下的分布鲁棒稀疏投资组合优化模型","authors":"Zhongyan Wang, Xiaodong Zhu, Shaojian Qu, M. Faisal Nadeem, Beibei Zhang","doi":"10.3934/mfc.2023043","DOIUrl":null,"url":null,"abstract":"We propose a distributionally robust portfolio optimization model with cardinality constraints under the satisfaction criterion. We aim to maximize the probability of achieving the target return of the proposed portfolio selection model while the number of assets the investors hold is limited. For practical significance, we cite a measure of shortfall-aware aspiration level to the portfolio optimization problem and convert it into a CVaR measure. In our model, we consider a worst-case and assume the distribution of returns of assets is ambiguous. We reformulate the CVaR-based measure equivalently to semi-definite programming for its tractability. A Benders' decomposition algorithm is designed to solve the proposed model efficiently. Numerical tests are utilized through actual market data to validate the proposed method. The results indicate that our algorithm can effectively solve the proposed model, and the sparse portfolio selection model under the satisfaction criterion achieves high robustness and perform better than classical models. Furthermore, we prove that taking the number of assets as the decision variable is a much more efficient method.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Distributionally robust sparse portfolio optimization model under satisfaction criterion\",\"authors\":\"Zhongyan Wang, Xiaodong Zhu, Shaojian Qu, M. Faisal Nadeem, Beibei Zhang\",\"doi\":\"10.3934/mfc.2023043\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a distributionally robust portfolio optimization model with cardinality constraints under the satisfaction criterion. We aim to maximize the probability of achieving the target return of the proposed portfolio selection model while the number of assets the investors hold is limited. For practical significance, we cite a measure of shortfall-aware aspiration level to the portfolio optimization problem and convert it into a CVaR measure. In our model, we consider a worst-case and assume the distribution of returns of assets is ambiguous. We reformulate the CVaR-based measure equivalently to semi-definite programming for its tractability. A Benders' decomposition algorithm is designed to solve the proposed model efficiently. Numerical tests are utilized through actual market data to validate the proposed method. The results indicate that our algorithm can effectively solve the proposed model, and the sparse portfolio selection model under the satisfaction criterion achieves high robustness and perform better than classical models. Furthermore, we prove that taking the number of assets as the decision variable is a much more efficient method.\",\"PeriodicalId\":93334,\"journal\":{\"name\":\"Mathematical foundations of computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical foundations of computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/mfc.2023043\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical foundations of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/mfc.2023043","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Distributionally robust sparse portfolio optimization model under satisfaction criterion
We propose a distributionally robust portfolio optimization model with cardinality constraints under the satisfaction criterion. We aim to maximize the probability of achieving the target return of the proposed portfolio selection model while the number of assets the investors hold is limited. For practical significance, we cite a measure of shortfall-aware aspiration level to the portfolio optimization problem and convert it into a CVaR measure. In our model, we consider a worst-case and assume the distribution of returns of assets is ambiguous. We reformulate the CVaR-based measure equivalently to semi-definite programming for its tractability. A Benders' decomposition algorithm is designed to solve the proposed model efficiently. Numerical tests are utilized through actual market data to validate the proposed method. The results indicate that our algorithm can effectively solve the proposed model, and the sparse portfolio selection model under the satisfaction criterion achieves high robustness and perform better than classical models. Furthermore, we prove that taking the number of assets as the decision variable is a much more efficient method.