{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T20:16:51Z","timestamp":1770754611687,"version":"3.50.0"},"reference-count":38,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,21]],"date-time":"2022-05-21T00:00:00Z","timestamp":1653091200000},"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":["Entropy"],"abstract":"<jats:p>In this paper, we propose a new optimal control model for uncertain systems with jump. In the model, the background-state variables are incorporated, where the background-state variables are governed by an uncertain differential equation. Meanwhile, the state variables are governed by another uncertain differential equation with jump, in which both the background-state variables and the control variables are involved. Under the optimistic value criterion, using uncertain dynamic programming method, we establish the principle and the equation of optimality. As an application, the optimal investment strategy and optimal payment rate for DC pension plans are given, where the corresponding background-state variables represent the salary process. This application in DC pension plans illustrates the effectiveness of the proposed model.<\/jats:p>","DOI":"10.3390\/e24050734","type":"journal-article","created":{"date-parts":[[2022,5,21]],"date-time":"2022-05-21T09:18:08Z","timestamp":1653124688000},"page":"734","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Control of Background-Based Uncertain Systems with Applications in DC Pension Plan"],"prefix":"10.3390","volume":"24","author":[{"given":"Wei","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China"}]},{"given":"Wanying","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China"}]},{"given":"Xiaoyi","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China"}]},{"given":"Yijun","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/0022-0531(71)90038-X","article-title":"Optimum consumption and portfolio rules in a continuous-time model","volume":"3","author":"Merton","year":"1971","journal-title":"J. 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