{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T15:09:51Z","timestamp":1762182591999,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Startup Foundation for Introducing Talent of NUIST","award":["1513142501025"],"award-info":[{"award-number":["1513142501025"]}]},{"name":"Hainan Province Higher Education Institutions Education and Teaching Reform Research Project","award":["Hnjg2025ZD-12"],"award-info":[{"award-number":["Hnjg2025ZD-12"]}]},{"name":"Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the development of uncertain finance, uncertain stock models have become increasingly popular for modeling stock prices. This paper explores the symmetric properties inherent in the uncertain mean-reverting stock model, particularly in the structure of its differential equations and the resulting pricing formulas. The primary findings comprise the derivation of explicit pricing formulas, via uncertain differential equations, for European, American, Asian, and geometric average Asian options under the uncertain mean-reverting stock model. The symmetry in the inverse uncertainty distributions and the duality between call and put options are highlighted, demonstrating the model\u2019s alignment with symmetric financial principles. Furthermore, several numerical examples are provided to illustrate the applicability and the symmetry-related characteristics of the derived formulas.<\/jats:p>","DOI":"10.3390\/sym17111830","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:47:58Z","timestamp":1762177678000},"page":"1830","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Option Pricing Formulas of Uncertain Mean-Reverting Stock Model with Symmetry Analysis"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0298-5996","authenticated-orcid":false,"given":"Yuxing","family":"Jia","sequence":"first","affiliation":[{"name":"School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China"}]},{"given":"Kaixi","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"}]},{"given":"Jinsheng","family":"Xie","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"}]},{"given":"Yuhan","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Tongji University, Shanghai 200092, China"}]},{"given":"Lifang","family":"Hong","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Hainan University, Haikou 570228, China"},{"name":"Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Hainan University, Haikou 570228, China"}]},{"given":"Zhigang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Hainan University, Haikou 570228, China"},{"name":"Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Hainan University, Haikou 570228, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,1]]},"reference":[{"key":"ref_1","unstructured":"Liu, B. 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