{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T12:49:00Z","timestamp":1765889340426,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T00:00:00Z","timestamp":1718064000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100015690","name":"DRPM Universitas Padjadjaran","doi-asserted-by":"publisher","award":["1549\/UN6.3.1\/PT.00\/2023","UniSZA\/2023\/FELLOWPENELIDIKAN(011)"],"award-info":[{"award-number":["1549\/UN6.3.1\/PT.00\/2023","UniSZA\/2023\/FELLOWPENELIDIKAN(011)"]}],"id":[{"id":"10.13039\/501100015690","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper aims to design a quadratic optimization model of an investment portfolio based on value-at-risk (VaR) by entering risk-free assets and company liabilities. The designed model develops Markowitz\u2019s investment portfolio optimization model with risk aversion. Model development was carried out using vector and matrix equations. The entry of risk-free assets and liabilities is essential. Risk-free assets reduce the loss risk, while liabilities accommodate a fundamental analysis of the company\u2019s condition. The model can be applied in various sectors of capital markets worldwide. This study applied the model to Indonesia\u2019s mining and energy sector. The application results show that risk aversion negatively correlates with the mean and VaR of the return of investment portfolios. Assuming that risk aversion is in the 5.1% to 8.2% interval, the maximum mean and VaR obtained for the next month are 0.0103316 and 0.0138270, respectively, while the minimum mean and VaR are 0.0102964 and 0.0137975, respectively. The finding of this study is that the vector equation for investment portfolio weights is obtained, which can facilitate calculating investment portfolio weight optimization. This study is expected to help investors control the quality of appropriate investment, especially in some stocks in Indonesia\u2019s mining and energy sector.<\/jats:p>","DOI":"10.3390\/computation12060120","type":"journal-article","created":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T11:58:58Z","timestamp":1718107138000},"page":"120","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Modeling of Mean-Value-at-Risk Investment Portfolio Optimization Considering Liabilities and Risk-Free Assets"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2608-9712","authenticated-orcid":false,"family":"Sukono","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia"},{"name":"Faculty of Business and Management, Universiti Sultan Zainal Abidin, Kuala Terengganu 21300, Malaysia"}]},{"given":"Puspa Liza Binti","family":"Ghazali","sequence":"additional","affiliation":[{"name":"Faculty of Business and Management, Universiti Sultan Zainal Abidin, Kuala Terengganu 21300, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2051-0695","authenticated-orcid":false,"given":"Muhamad Deni","family":"Johansyah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8999-9508","authenticated-orcid":false,"family":"Riaman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2686-1752","authenticated-orcid":false,"given":"Riza Andrian","family":"Ibrahim","sequence":"additional","affiliation":[{"name":"Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia"}]},{"given":"Mustafa","family":"Mamat","sequence":"additional","affiliation":[{"name":"Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Kuala Terengganu 21300, Malaysia"}]},{"given":"Aceng","family":"Sambas","sequence":"additional","affiliation":[{"name":"Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Kuala Terengganu 21300, Malaysia"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"59","DOI":"10.54259\/ijba.v1i1.22","article-title":"Portfolio Optimization Based on Clustering of Indonesia Stock Exchange: A Case Study of Index LQ45","volume":"1","author":"Siregar","year":"2021","journal-title":"Indones. 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