{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T02:50:24Z","timestamp":1779936624223,"version":"3.53.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"23","license":[{"start":{"date-parts":[[2021,9,12]],"date-time":"2021-09-12T00:00:00Z","timestamp":1631404800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,9,12]],"date-time":"2021-09-12T00:00:00Z","timestamp":1631404800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s00500-021-06214-1","type":"journal-article","created":{"date-parts":[[2021,9,12]],"date-time":"2021-09-12T13:05:37Z","timestamp":1631451937000},"page":"14785-14795","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Lookback option pricing problem of uncertain mean-reverting currency model"],"prefix":"10.1007","volume":"25","author":[{"given":"Yang","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liying","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,9,12]]},"reference":[{"key":"6214_CR1","first-page":"21","volume":"17","author":"L Bachelier","year":"1900","unstructured":"Bachelier L (1900) Theory of speculation. Annales Sci Econimic 17:21\u201386","journal-title":"Annales Sci Econimic"},{"key":"6214_CR2","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1086\/260062","volume":"81","author":"F Black","year":"1973","unstructured":"Black F, Scholes M (1973) The pricing of option and corporate liabilities. J Political Econ 81:637\u2013654","journal-title":"J Political Econ"},{"issue":"2","key":"6214_CR3","first-page":"32","volume":"8","author":"XW Chen","year":"2011","unstructured":"Chen XW (2011) American option pricing formula for uncertain financial market. Int J Oper Res 8(2):32\u201337","journal-title":"Int J Oper Res"},{"key":"6214_CR4","doi-asserted-by":"publisher","first-page":"1893","DOI":"10.1111\/j.1540-6261.1991.tb04648.x","volume":"46","author":"A Conze","year":"1991","unstructured":"Conze A, Viswanathan R (1991) Path dependent options: the case of lookback options. J Finance 46:1893\u20131907","journal-title":"J Finance"},{"key":"6214_CR5","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1111\/j.0960-1627.2004.00199.x","volume":"14","author":"M Dai","year":"2004","unstructured":"Dai M, Wong HY, Kwok YK (2004) Quanto lookback options. Math Finance 14:445\u2013467","journal-title":"Math Finance"},{"key":"6214_CR6","doi-asserted-by":"publisher","first-page":"5647","DOI":"10.1007\/s00500-017-2558-y","volume":"22","author":"Y Gao","year":"2018","unstructured":"Gao Y, Yang XF, Fu ZF (2018) Lookback option pricing problem of uncertain exponential Ornstein-Uhlenbeck model. Soft Comput 22:5647\u20135654","journal-title":"Soft Comput"},{"key":"6214_CR7","first-page":"1111","volume":"34","author":"MB Goldman","year":"1979","unstructured":"Goldman MB, Sosin HB, Gatto MA (1979) Path dependent options: buy at the low, sell at the high. J Finance 34:1111\u20131127","journal-title":"J Finance"},{"key":"6214_CR8","first-page":"1","volume":"4","author":"K Ito","year":"1951","unstructured":"Ito K (1951) On stochastic differential equations. Am Math Soc 4:1\u201351","journal-title":"Am Math Soc"},{"key":"6214_CR9","doi-asserted-by":"crossref","unstructured":"Liu B (2013), Toward uncertain finance theory, J Uncertainty Anal Appl1 , Article 1","DOI":"10.1186\/2195-5468-1-1"},{"key":"6214_CR10","volume-title":"Uncertain Theory","author":"B Liu","year":"2007","unstructured":"Liu B (2007) Uncertain Theory, 2nd edn. Springer-Verlag, Berlin","edition":"2"},{"issue":"1","key":"6214_CR11","first-page":"3","volume":"2","author":"B Liu","year":"2008","unstructured":"Liu B (2008) Fuzzy process, hybrid process and uncertain process. J Uncertain Syst 2(1):3\u201316","journal-title":"J Uncertain Syst"},{"issue":"1","key":"6214_CR12","first-page":"3","volume":"3","author":"B Liu","year":"2009","unstructured":"Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3\u201310","journal-title":"J Uncertain Syst"},{"key":"6214_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-89484-1","volume-title":"Theory and practice of uncertain programming","author":"B Liu","year":"2009","unstructured":"Liu B (2009) Theory and practice of uncertain programming, 2nd edn. Springer-Verlag, Berlin","edition":"2"},{"key":"6214_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13959-8","volume-title":"Uncertainty theory: a branch of mathematics for modeling human uncertainty","author":"B Liu","year":"2010","unstructured":"Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer-Verlag, Berlin"},{"issue":"3","key":"6214_CR15","first-page":"163","volume":"4","author":"B Liu","year":"2010","unstructured":"Liu B (2010) Uncertain risk analysis and uncertain reliability analysis. J Uncertain Syst 4(3):163\u2013170","journal-title":"J Uncertain Syst"},{"issue":"1","key":"6214_CR16","first-page":"3","volume":"5","author":"B Liu","year":"2011","unstructured":"Liu B (2011) Uncertain logic for modeling human language. J Uncertain Syst 5(1):3\u201320","journal-title":"J Uncertain Syst"},{"issue":"3","key":"6214_CR17","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s10700-014-9181-5","volume":"13","author":"B Liu","year":"2014","unstructured":"Liu B (2014) Uncertainty distribution and independence on uncertain processes. Fuzzy Optim Decision Making 13(3):259\u2013271","journal-title":"Fuzzy Optim Decision Making"},{"issue":"4","key":"6214_CR18","doi-asserted-by":"publisher","first-page":"4845","DOI":"10.3233\/JIFS-191535","volume":"38","author":"Y Liu","year":"2020","unstructured":"Liu Y, Lio W (2020) A revision of sufficient and necessary condition of uncertainty distribution. J Intell Fuzzy Syst 38(4):4845\u20134854","journal-title":"J Intell Fuzzy Syst"},{"issue":"1","key":"6214_CR19","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1002\/int.21680","volume":"30","author":"Y Liu","year":"2015","unstructured":"Liu Y, Chen X, Ralescu DA (2015) Uncetain currency model and currency option pricing. Int J Intell Syst 30(1):40\u201351","journal-title":"Int J Intell Syst"},{"key":"6214_CR20","doi-asserted-by":"crossref","unstructured":"Merton RC (1973) Theory of rational option pricing. Bell J Econ Manag Sci 4:141\u2013183","DOI":"10.2307\/3003143"},{"issue":"10","key":"6214_CR21","doi-asserted-by":"publisher","first-page":"4131","DOI":"10.1007\/s00500-015-1748-8","volume":"20","author":"YY Shen","year":"2016","unstructured":"Shen YY, Yao K (2016) A mean-reverting currency model in an uncertain environment. Soft Comput 20(10):4131\u20134138","journal-title":"Soft Comput"},{"key":"6214_CR22","doi-asserted-by":"publisher","first-page":"4261","DOI":"10.3233\/JIFS-17536","volume":"34","author":"YH Sheng","year":"2018","unstructured":"Sheng YH, Shi G (2018) Mean-reverting stock model and pricingrules for Asian currency option. J Intell Fuzzy Syst 34:4261\u20134268","journal-title":"J Intell Fuzzy Syst"},{"key":"6214_CR23","doi-asserted-by":"crossref","unstructured":"Sun JJ, Chen XW (2015), Asian option pricing formula for uncertain financial market, J Uncertain Anal Appl3 , Article 11","DOI":"10.1186\/s40467-015-0035-7"},{"key":"6214_CR24","doi-asserted-by":"publisher","first-page":"6739","DOI":"10.1007\/s00500-016-2224-9","volume":"21","author":"X Wang","year":"2017","unstructured":"Wang X, Ning YF (2017) An uncertain currency model with floating interest rates. Soft Comput 21:6739\u20136754","journal-title":"Soft Comput"},{"key":"6214_CR25","doi-asserted-by":"crossref","unstructured":"Yao K (2013), Extreme values and integral of solution of uncertain differential equation, J Uncertain Anal Appl1 , Article 2","DOI":"10.1186\/2195-5468-1-2"},{"issue":"3","key":"6214_CR26","doi-asserted-by":"publisher","first-page":"825","DOI":"10.3233\/IFS-120688","volume":"25","author":"K Yao","year":"2013","unstructured":"Yao K, Chen X (2013) A numerical method for solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825\u2013832","journal-title":"J Intell Fuzzy Syst"},{"issue":"4","key":"6214_CR27","first-page":"317","volume":"8","author":"ZQ Zhang","year":"2014","unstructured":"Zhang ZQ, Liu WQ (2014) Geometric average Asian option pricing for uncertain financial market. J Uncertain Syst 8(4):317\u2013320","journal-title":"J Uncertain Syst"},{"key":"6214_CR28","doi-asserted-by":"publisher","first-page":"5537","DOI":"10.1007\/s00500-018-3211-0","volume":"23","author":"ZQ Zhang","year":"2019","unstructured":"Zhang ZQ, Ke H, Liu WQ (2019) Lookback options pricing for uncertain financial market. Soft Comput 23:5537\u20135546","journal-title":"Soft Comput"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06214-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-021-06214-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06214-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T18:18:44Z","timestamp":1635185924000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-021-06214-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,12]]},"references-count":28,"journal-issue":{"issue":"23","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["6214"],"URL":"https:\/\/doi.org\/10.1007\/s00500-021-06214-1","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,12]]},"assertion":[{"value":"22 August 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 September 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Human or animal rights"}}]}}