{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:45:29Z","timestamp":1760784329239,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"17","license":[{"start":{"date-parts":[[2017,7,28]],"date-time":"2017-07-28T00:00:00Z","timestamp":1501200000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"National Natural Science Foundation of China (CN)","award":["61673225"],"award-info":[{"award-number":["61673225"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61304182","61374082"],"award-info":[{"award-number":["61304182","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":[[2018,9]]},"DOI":"10.1007\/s00500-017-2737-x","type":"journal-article","created":{"date-parts":[[2017,7,27]],"date-time":"2017-07-27T23:53:28Z","timestamp":1501199608000},"page":"5835-5841","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Two-factor term structure model with uncertain volatility risk"],"prefix":"10.1007","volume":"22","author":[{"given":"Xiaowei","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinwu","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,7,28]]},"reference":[{"issue":"1","key":"2737_CR1","doi-asserted-by":"crossref","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":"4","key":"2737_CR2","doi-asserted-by":"crossref","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(4):597\u2013604","journal-title":"Soft Comput"},{"issue":"10","key":"2737_CR3","doi-asserted-by":"crossref","first-page":"2905","DOI":"10.1007\/s00500-014-1452-0","volume":"19","author":"X Chen","year":"2015","unstructured":"Chen X (2015) Uncertain calculus with finite variation processes. Soft Comput 19(10):2905\u20132912","journal-title":"Soft Comput"},{"key":"2737_CR4","unstructured":"Chen X (2016) Nested uncertain differential equations and its application to multi-factor term structure model. http:\/\/orsc.edu.cn\/online\/160104.pdf"},{"key":"2737_CR5","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/0304-405X(78)90020-X","volume":"6","author":"L Dothan","year":"1978","unstructured":"Dothan L (1978) On the term structure of interest rates. J Financ Econ 6:59\u201369","journal-title":"J Financ Econ"},{"key":"2737_CR6","volume-title":"Interest rate modelling","author":"J James","year":"2000","unstructured":"James J, Webber N (2000) Interest rate modelling. Wiley-Blackwell Publishing, Oxford"},{"issue":"3","key":"2737_CR7","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1007\/s00500-014-1301-1","volume":"19","author":"D Jiao","year":"2015","unstructured":"Jiao D, Yao K (2015) An interest rate model in uncertain environment. Soft Comput 19(3):775\u2013780","journal-title":"Soft Comput"},{"key":"2737_CR8","volume-title":"Uncertainty theory","author":"B Liu","year":"2007","unstructured":"Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin","edition":"2"},{"issue":"1","key":"2737_CR9","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"},{"key":"2737_CR10","unstructured":"Liu B (2009a) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3\u201310"},{"key":"2737_CR11","doi-asserted-by":"crossref","unstructured":"Liu B (2009b) Theory and practice of uncertain programming, 2nd edn. Springer, Berlin","DOI":"10.1007\/978-3-540-89484-1"},{"key":"2737_CR12","doi-asserted-by":"crossref","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"},{"issue":"1","key":"2737_CR13","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1002\/int.21680","volume":"30","author":"Y Liu","year":"2015","unstructured":"Liu Y, Chen X, Ralescu DA (2015) Uncertain currency model and currency option pricing. Int J Intell Syst 30(1):40\u201351","journal-title":"Int J Intell Syst"},{"issue":"2","key":"2737_CR14","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1111\/j.1540-6261.1983.tb02275.x","volume":"38","author":"T Marsh","year":"1983","unstructured":"Marsh T, Rosenfeld E (1983) Stochastic processes for interest rates and equilibrium bond prices. J Financ 38(2):635\u2013646","journal-title":"J Financ"},{"issue":"1","key":"2737_CR15","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1007\/BF02846028","volume":"4","author":"G Maruyama","year":"1955","unstructured":"Maruyama G (1955) Continuous Markov processes and stochastic equations. Rend Circolo Mat Palermo 4(1):48\u201390","journal-title":"Rend Circolo Mat Palermo"},{"key":"2737_CR16","doi-asserted-by":"crossref","first-page":"141","DOI":"10.2307\/3003143","volume":"4","author":"R Merton","year":"1973","unstructured":"Merton R (1973) Theory of rational option pricing. Bell J Econ Manag Sci 4:141\u2013183","journal-title":"Bell J Econ Manag Sci"},{"issue":"3","key":"2737_CR17","first-page":"557","volume":"19","author":"GN Milstein","year":"1974","unstructured":"Milstein GN (1974) Approximate integration of stochastic differential equations. Theory Probab Appl 19(3):557\u2013562","journal-title":"Theory Probab Appl"},{"issue":"2","key":"2737_CR18","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(2):18\u201326","journal-title":"Int J Oper Res"},{"issue":"3","key":"2737_CR19","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1137\/0719041","volume":"19","author":"W Rumelin","year":"1982","unstructured":"Rumelin W (1982) Numerical treatment of stochastic differential equations. SIAM J Numer Anal 19(3):604\u2013613","journal-title":"SIAM J Numer Anal"},{"key":"2737_CR20","doi-asserted-by":"crossref","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"},{"issue":"3","key":"2737_CR21","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s10700-012-9132-y","volume":"11","author":"K Yao","year":"2012","unstructured":"Yao K (2012) Uncertain calculus with renewal process. Fuzzy Optim Decis Mak 11(3):285\u2013297","journal-title":"Fuzzy Optim Decis Mak"},{"issue":"3","key":"2737_CR22","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(3):825\u2013832","journal-title":"J Intell Fuzzy Syst"},{"issue":"1","key":"2737_CR23","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10700-012-9139-4","volume":"12","author":"K Yao","year":"2013","unstructured":"Yao K, Gao J, Gao Y (2013) Some stability theorems of uncertain differential equation. Fuzzy Optim Decis Mak 12(1):3\u201313","journal-title":"Fuzzy Optim Decis Mak"},{"issue":"4","key":"2737_CR24","first-page":"244","volume":"8","author":"K Yao","year":"2014","unstructured":"Yao K (2014) Multi-dimensional uncertain calculus with Liu process. J Uncertain Syst 8(4):244\u2013254","journal-title":"J Uncertain Syst"},{"issue":"4","key":"2737_CR25","doi-asserted-by":"crossref","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(4):399\u2013424","journal-title":"Fuzzy Optim Decis Mak"},{"issue":"2","key":"2737_CR26","doi-asserted-by":"crossref","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(2):139\u2013154","journal-title":"Fuzzy Optim Decis Mak"},{"issue":"7","key":"2737_CR27","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1080\/01969722.2010.511552","volume":"41","author":"Y Zhu","year":"2010","unstructured":"Zhu Y (2010) Uncertain optimal control with application to a portfolio selection model. Cybern Syst 41(7):535\u2013547","journal-title":"Cybern Syst"},{"issue":"15","key":"2737_CR28","doi-asserted-by":"crossref","first-page":"3359","DOI":"10.1002\/mma.3335","volume":"38","author":"Y Zhu","year":"2015","unstructured":"Zhu Y (2015) Uncertain fractional differential equations and an interest rate model. Math Methods Appl Sci 38(15):3359\u20133368","journal-title":"Math Methods Appl Sci"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-017-2737-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-017-2737-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-017-2737-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,13]],"date-time":"2020-10-13T14:37:47Z","timestamp":1602599867000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-017-2737-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,28]]},"references-count":28,"journal-issue":{"issue":"17","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["2737"],"URL":"https:\/\/doi.org\/10.1007\/s00500-017-2737-x","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2017,7,28]]}}}