{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T00:41:39Z","timestamp":1767832899831,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T00:00:00Z","timestamp":1690416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11961064"],"award-info":[{"award-number":["11961064"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper considers the problem of portfolio selection and adjustment for target benefit plans (TBP) with longevity trends and partial information. The longevity trends are modeled by a time-varying force function. The financial market consists of risk-free assets and stocks, in which the return rate of stocks is a stochastic process and cannot be completely observed. This paper adopts the mean-variance utility model as an optimization criterion. The aim is to maximize the terminal value of the pension fund and the excess pension benefit after the participant\u2019s retirement. The optimization equations are developed in game theory to obtain explicit solutions for the equilibrium strategies. Finally, the influence of the longevity trend on the internal structure of the pension system and the sensitivity of the equilibrium strategies to the related parameters are explored by numerical analysis. The conclusion shows that this model\u2019s results can provide stable and adequate retirement benefits for participants.<\/jats:p>","DOI":"10.3390\/axioms12080732","type":"journal-article","created":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T02:10:45Z","timestamp":1690510245000},"page":"732","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An Equilibrium Strategy for Target Benefit Pension Plans with a Longevity Trend and Partial Information"],"prefix":"10.3390","volume":"12","author":[{"given":"Wei","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-6990-5146","authenticated-orcid":false,"given":"Na","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2596-9489","authenticated-orcid":false,"given":"Ahmadjan","family":"Muhammadhaji","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1080\/03017605.2022.2123605","article-title":"Understanding Money & Credit in Contemporary Capitalism: Back to the Future of Marx\u2019s Theory of Fetishism and Alienation","volume":"50","author":"Meramveliotakis","year":"2011","journal-title":"Critique"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1080\/13501763.2019.1575455","article-title":"The political economy of pension financialisation: Public policy responses to the crisis","volume":"26","author":"Hassel","year":"2019","journal-title":"J. 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