{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T23:11:29Z","timestamp":1773702689486,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"16","license":[{"start":{"date-parts":[[2018,2,9]],"date-time":"2018-02-09T00:00:00Z","timestamp":1518134400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61374082"],"award-info":[{"award-number":["61374082"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2018,8]]},"DOI":"10.1007\/s00500-018-3028-x","type":"journal-article","created":{"date-parts":[[2018,2,9]],"date-time":"2018-02-09T04:43:07Z","timestamp":1518151387000},"page":"5335-5346","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["International investing in uncertain financial market"],"prefix":"10.1007","volume":"22","author":[{"given":"Yi","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4806-927X","authenticated-orcid":false,"given":"Jinwu","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"An","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,2,9]]},"reference":[{"key":"3028_CR1","doi-asserted-by":"publisher","first-page":"24","DOI":"10.2307\/3664834","volume":"12","author":"N Biger","year":"1983","unstructured":"Biger N, Hull J (1983) The valuation of currency options. Financ Manag 12:24\u201328","journal-title":"Financ Manag"},{"key":"3028_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 Polit Econ 81:637\u2013654","journal-title":"J Polit Econ"},{"issue":"2","key":"3028_CR3","first-page":"32","volume":"8","author":"X Chen","year":"2011","unstructured":"Chen X (2011) American option pricing formula for uncertain financial market. Int J Oper Res 8(2):32\u201337","journal-title":"Int J Oper Res"},{"key":"3028_CR4","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s00500-012-0927-0","volume":"17","author":"X Chen","year":"2013","unstructured":"Chen X, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17:597\u2013604","journal-title":"Soft Comput"},{"issue":"1","key":"3028_CR5","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s10700-010-9073-2","volume":"9","author":"X Chen","year":"2010","unstructured":"Chen X, Liu B (2010) Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optim Decis Mak 9(1):69\u201381","journal-title":"Fuzzy Optim Decis Mak"},{"issue":"1","key":"3028_CR6","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s10700-012-9141-x","volume":"12","author":"X Chen","year":"2013","unstructured":"Chen X, Liu Y, Ralescu D (2013) Uncertain stock model with periodic dividends. Fuzzy Optim Decis Mak 12(1):111\u2013123","journal-title":"Fuzzy Optim Decis Mak"},{"key":"3028_CR7","doi-asserted-by":"publisher","first-page":"385","DOI":"10.2307\/1911242","volume":"53","author":"J Cox","year":"1985","unstructured":"Cox J, Ingersoll J, Ross S (1985) A theory of the term structure of interest rates. Econometrica 53:385\u2013408","journal-title":"Econometrica"},{"key":"3028_CR8","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/BF01450498","volume":"300","author":"F Delbaen","year":"1999","unstructured":"Delbaen F, Schachermayer W (1999) A general version of the fundamental theorem of asset pricing. Math Ann 300:463\u2013520","journal-title":"Math Ann"},{"issue":"1","key":"3028_CR9","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s10700-012-9145-6","volume":"12","author":"J Gao","year":"2013","unstructured":"Gao J (2013) Uncertain bimatrix game with applications. Fuzzy Optim Decis Mak 12(1):65\u201378","journal-title":"Fuzzy Optim Decis Mak"},{"key":"3028_CR10","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/0022-0531(79)90043-7","volume":"20","author":"M Harrison","year":"1979","unstructured":"Harrison M, Kreps D (1979) Martingales and arbitrage in multiperiod securities markets. J Econ Theory 20:381\u2013408","journal-title":"J Econ Theory"},{"key":"3028_CR11","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/0304-4149(81)90026-0","volume":"11","author":"M Harrison","year":"1981","unstructured":"Harrison M, Pliska S (1981) Martingales and stochastic integrals in the theory of continuous trading. Stoch Process Appl 11:215\u2013260","journal-title":"Stoch Process Appl"},{"issue":"18","key":"3028_CR12","doi-asserted-by":"publisher","first-page":"5507","DOI":"10.1007\/s00500-016-2141-y","volume":"21","author":"X Ji","year":"2017","unstructured":"Ji X, Wu H (2017) A currency exchange rate model with jumps in uncertain environment. Soft Comput 21(18):5507\u20135514","journal-title":"Soft Comput"},{"key":"3028_CR13","volume-title":"Uncertainty theory","author":"B Liu","year":"2007","unstructured":"Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin","edition":"2"},{"key":"3028_CR14","first-page":"3","volume":"2","author":"B Liu","year":"2008","unstructured":"Liu B (2008) Fuzzy process, hybrid process and uncertain process. J Uncertain Syst 2:3\u201316","journal-title":"J Uncertain Syst"},{"key":"3028_CR15","first-page":"3","volume":"3","author":"B Liu","year":"2009","unstructured":"Liu B (2009a) Some research problems in uncertainty theory. J Uncertain Syst 3:3\u201310","journal-title":"J Uncertain Syst"},{"key":"3028_CR16","doi-asserted-by":"crossref","unstructured":"Liu (2009b) Theory and practice of uncertain programming. Springer, Berlin","DOI":"10.1007\/978-3-540-89484-1_7"},{"key":"3028_CR17","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, Berlin"},{"key":"3028_CR18","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 of uncertain processes. Fuzzy Optim Decis Mak 13:259\u2013271","journal-title":"Fuzzy Optim Decis Mak"},{"key":"3028_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 D (2015) Uncertain currency model and currency option pricing. Int J Intell Syst 30:40\u201351","journal-title":"Int J Intell Syst"},{"key":"3028_CR20","doi-asserted-by":"publisher","first-page":"247","DOI":"10.2307\/1926560","volume":"51","author":"R Merton","year":"1969","unstructured":"Merton R (1969) Lifetime portfolio selection under uncertainty: the continuous time case. Rev Econ Stat 51:247\u2013257","journal-title":"Rev Econ Stat"},{"key":"3028_CR21","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/0167-2231(79)90034-4","volume":"11","author":"M Mussa","year":"1979","unstructured":"Mussa M (1979) Empirical regularities in the behavior of exchange rates and theories of the foreign exchange market. Carnegie Rochester Ser Public Policy 11:9\u201357","journal-title":"Carnegie Rochester Ser Public Policy"},{"key":"3028_CR22","first-page":"18","volume":"8","author":"J Peng","year":"2011","unstructured":"Peng J, Yao K (2011) A new option pricing model for stocks in uncertainty markets. Int J Oper Res 8:18\u201326","journal-title":"Int J Oper Res"},{"key":"3028_CR23","doi-asserted-by":"publisher","first-page":"4131","DOI":"10.1007\/s00500-015-1748-8","volume":"20","author":"Y Shen","year":"2016","unstructured":"Shen Y, Yao K (2016) A mean-reverting currency model in an uncertain environment. Soft Comput 20:4131\u20134138","journal-title":"Soft Comput"},{"key":"3028_CR24","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1186\/s40467-015-0035-7","volume":"3","author":"J Sun","year":"2015","unstructured":"Sun J, Chen X (2015) Asian option pricing formula for uncertain financial market. J Uncertain Anal Appl 3:11","journal-title":"J Uncertain Anal Appl"},{"key":"3028_CR25","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/0304-405X(77)90016-2","volume":"5","author":"O Vasicek","year":"1977","unstructured":"Vasicek O (1977) An equilibrium characterization of the term structure. J Financ Econ 5:177\u2013188","journal-title":"J Financ Econ"},{"key":"3028_CR26","doi-asserted-by":"publisher","first-page":"1186","DOI":"10.3390\/su8111186","volume":"8","author":"C Xiao","year":"2016","unstructured":"Xiao C, Zhang Y, Fu Z (2016) Valuing interest rate swap contracts in uncertain financial market. Sustainability 8:1186\u20131196","journal-title":"Sustainability"},{"key":"3028_CR27","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/s10700-015-9211-y","volume":"14","author":"K Yao","year":"2015","unstructured":"Yao K (2015) Uncertain contour process and its application in stock model with floating interest rate. Fuzzy Optim Decis Mak 14:399\u2013424","journal-title":"Fuzzy Optim Decis Mak"},{"key":"3028_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-52729-0","volume-title":"Uncertain differential equations","author":"K Yao","year":"2016","unstructured":"Yao K (2016) Uncertain differential equations. Springer, Berlin"},{"key":"3028_CR29","doi-asserted-by":"crossref","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 25:825\u2013832","journal-title":"J Intell Fuzzy Syst"},{"key":"3028_CR30","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1142\/S0218488512500213","volume":"20","author":"X Yu","year":"2012","unstructured":"Yu X (2012) A stock model with jumps for uncertain markets. Int J Uncertain Fuzziness Knowl Based Syst 20:421\u2013432","journal-title":"Int J Uncertain Fuzziness Knowl Based Syst"},{"key":"3028_CR31","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s10700-015-9223-7","volume":"15","author":"Z Zhang","year":"2016","unstructured":"Zhang Z, Ralescu D, Liu W (2016) Valuation of interest rate ceiling and floor in uncertain financial market. Fuzzy Optim Decis Mak 15:139\u2013154","journal-title":"Fuzzy Optim Decis Mak"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-018-3028-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-018-3028-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-018-3028-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,27]],"date-time":"2020-10-27T23:38:13Z","timestamp":1603841893000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-018-3028-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,9]]},"references-count":31,"journal-issue":{"issue":"16","published-print":{"date-parts":[[2018,8]]}},"alternative-id":["3028"],"URL":"https:\/\/doi.org\/10.1007\/s00500-018-3028-x","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,9]]},"assertion":[{"value":"9 February 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}