{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T08:50:28Z","timestamp":1782291028655,"version":"3.54.5"},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T00:00:00Z","timestamp":1763424000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We study two continuous-time, time-inconsistent problems for an individual who purchases life annuities and invests her wealth in a risky asset under the mean-variance criterion. In the first problem, the buyer may only purchase life annuities at a bounded, continuous rate, while in the second problem, the buyer may purchase any amount of life annuity income at any time, which results in a singular control problem. We find the individual\u2019s time-consistent equilibrium control strategies\n                    <jats:italic>explicitly<\/jats:italic>\n                    for the two life-annuity problems by solving the corresponding extended Hamilton\u2013Jacobi\u2013Bellman systems of equations. We also discuss the effects of parameters on the equilibrium strategies of the two life-annuity problems.\n                  <\/jats:p>","DOI":"10.1017\/jpr.2025.10044","type":"journal-article","created":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:46:05Z","timestamp":1763469965000},"page":"648-667","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Time-consistent annuitization and asset allocation under the mean-variance criterion"],"prefix":"10.1017","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5542-815X","authenticated-orcid":false,"given":"Xiaoqing","family":"Liang","sequence":"first","affiliation":[{"name":"Hebei University of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Virginia R.","family":"Young","sequence":"additional","affiliation":[{"name":"University of Michigan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,11,18]]},"reference":[{"key":"S0021900225100442_ref14","first-page":"77","article-title":"Portfolio selection","volume":"7","author":"Markowitz","year":"1952","journal-title":"J. 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Working paper, available at https:\/\/papers.ssrn.com\/sol3\/papers.cfm?abstract_id=1694759.","DOI":"10.2139\/ssrn.1694759"},{"key":"S0021900225100442_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.joep.2014.04.001"},{"key":"S0021900225100442_ref1","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhq028"},{"key":"S0021900225100442_ref2","doi-asserted-by":"publisher","DOI":"10.1080\/10920277.2009.10597543"},{"key":"S0021900225100442_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2023.06.003"},{"key":"S0021900225100442_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2012.06.002"},{"key":"S0021900225100442_ref11","doi-asserted-by":"publisher","DOI":"10.1137\/17M1153479"},{"key":"S0021900225100442_ref7","doi-asserted-by":"publisher","DOI":"10.1287\/moor.15.4.676"},{"key":"S0021900225100442_ref13","doi-asserted-by":"publisher","DOI":"10.1137\/23M1609701"},{"key":"S0021900225100442_ref5","volume-title":"Handbook of Brownian Motion \u2013 Facts and Formulae","author":"Borodin","year":"2012"},{"key":"S0021900225100442_ref8","first-page":"28","article-title":"Selection effects in the United Kingdom individual annuities market","volume":"112","author":"Finkelstein","year":"2002","journal-title":"Econom. J."}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900225100442","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T08:38:46Z","timestamp":1782290326000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900225100442\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,18]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["S0021900225100442"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2025.10044","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,18]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}