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Applying the stochastic optimal control technique, a Hamilton\u2013Jacobi\u2013Bellman (HJB) equation is derived. Then, the effective investment strategy and the minimum variance are obtained explicitly by using the Lagrange duality method. Moreover, some numerical examples are provided to verify the effectiveness of our results.<\/jats:p>","DOI":"10.1155\/2020\/1435356","type":"journal-article","created":{"date-parts":[[2020,3,23]],"date-time":"2020-03-23T23:30:43Z","timestamp":1585006243000},"page":"1-13","source":"Crossref","is-referenced-by-count":6,"title":["Portfolio Optimization with Asset-Liability Ratio Regulation Constraints"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8406-9210","authenticated-orcid":true,"given":"De-Lei","family":"Sheng","sequence":"first","affiliation":[{"name":"School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peilong","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Finance, Shanxi University of Finance and Economics, Taiyuan 030006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.3905\/jpm.1990.409248"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.2143\/ast.25.1.563252"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/s0165-1889(03)00067-8"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00100"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2006.03.006"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2009.01.005"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-017-0580-6"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2017.11.006"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2017.08.011"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1080\/10920277.2016.1247719"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2017.09.022"},{"key":"12","first-page":"329","volume":"442","year":"2015","journal-title":"Physica A"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jedc.2016.03.003"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1086\/260062"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.2307\/2978814"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jedc.2017.01.001"},{"key":"17","year":"1968"},{"key":"18","year":"2009"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.econmod.2015.07.017"},{"key":"20","year":"2016"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1002\/ijfe.1595"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1435356.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1435356.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1435356.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,23]],"date-time":"2020-03-23T23:30:45Z","timestamp":1585006245000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/1435356\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,23]]},"references-count":21,"alternative-id":["1435356","1435356"],"URL":"https:\/\/doi.org\/10.1155\/2020\/1435356","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,23]]}}}