{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T10:51:15Z","timestamp":1742640675432},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,1,4]],"date-time":"2019-01-04T00:00:00Z","timestamp":1546560000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2019,8]]},"DOI":"10.1007\/s11424-018-7300-z","type":"journal-article","created":{"date-parts":[[2019,1,10]],"date-time":"2019-01-10T04:30:51Z","timestamp":1547094651000},"page":"997-1018","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Optimal Control of Fully-Coupled Forward-Backward Doubly Stochastic Systems Driven by It\u00f4-L\u00e9vy Processes"],"prefix":"10.1007","volume":"32","author":[{"given":"Wencan","family":"Wang","sequence":"first","affiliation":[]},{"given":"Jinbiao","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Zaiming","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,1,4]]},"reference":[{"issue":"5-6","key":"7300_CR1","doi-asserted-by":"publisher","first-page":"939","DOI":"10.1007\/s13370-014-0248-9","volume":"26","author":"B \u00d8ksendal","year":"2015","unstructured":"\u00d8ksendal B and Sulem A, Risk minimization in financial markets modeled by It\u00f4\u2019s-L\u00e9vy processes, Afrika Matematika, 2015, 26(5-6): 939\u2013979.","journal-title":"Afrika Matematika"},{"issue":"3","key":"7300_CR2","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1214\/aoap\/1177005363","volume":"3","author":"F Antonelli","year":"1993","unstructured":"Antonelli F, Backward-forward stochastic differential equations, The Annals of Applied Probability, 1993, 3(3): 777\u2013793.","journal-title":"The Annals of Applied Probability"},{"issue":"3","key":"7300_CR3","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1007\/BF01192258","volume":"98","author":"J Ma","year":"1994","unstructured":"Ma J, Protter P, and Yong J M, Solving forward-backward stochastic differential equations explicitly \u2014 A four step scheme, Probability Theory and Related Fields, 1994, 98(3): 339\u2013359.","journal-title":"Probability Theory and Related Fields"},{"issue":"2","key":"7300_CR4","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/BF01195978","volume":"27","author":"S G Peng","year":"1993","unstructured":"Peng S G, Backward stochastic differential equations and applications to optimal control, Applied Mathematics & Optimization, 1993, 27(2): 125\u2013144.","journal-title":"Applied Mathematics & Optimization"},{"issue":"3","key":"7300_CR5","first-page":"249","volume":"11","author":"Z Wu","year":"1998","unstructured":"Wu Z, Maximum principle for optimal control problem of fully coupled forward-backward stochastic systems, Journal of Systems Science and Mathematical Sciences, 1998, 11(3): 249\u2013259.","journal-title":"Journal of Systems Science and Mathematical Sciences"},{"issue":"5","key":"7300_CR6","doi-asserted-by":"publisher","first-page":"1473","DOI":"10.1016\/j.automatica.2013.02.005","volume":"49","author":"Z Wu","year":"2013","unstructured":"Wu Z, A general maximum principle for optimal control of forward-backward stochastic systems, Automatica, 2013, 49(5): 1473\u20131480.","journal-title":"Automatica"},{"issue":"2","key":"7300_CR7","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/j.jmaa.2013.05.013","volume":"407","author":"S L Ji","year":"2013","unstructured":"Ji S L and Wei Q M, A maximum principle for fully coupled forward-backward stochastic control systems with terminal state constraints, Journal of Mathematical Analysis and Applications, 2013, 407(2): 200\u2013210.","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"3","key":"7300_CR8","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1137\/S0363012996313549","volume":"37","author":"S G Peng","year":"1999","unstructured":"Peng S G and Wu Z, Fully coupled forward-backward stochastic differential equations and applications to optimal control, SIAM Journal on Control and Optimization, 1999, 37(3): 825\u2013843.","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"2","key":"7300_CR9","first-page":"179","volume":"18","author":"Z Wu","year":"2005","unstructured":"Wu Z, Forward-backward stochastic differential equations, linear quadratic stochastic optimal control and nonzero sum differential games, Journal of Systems Science & Complexity, 2005, 18(2): 179\u2013192.","journal-title":"Journal of Systems Science & Complexity"},{"issue":"1","key":"7300_CR10","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1002\/asjc.406","volume":"14","author":"Z Y Yu","year":"2012","unstructured":"Yu Z Y, Linear-quadratic optimal control and nonzero-sum differential game of forward-backward stochastic system, Asian Journal of Control, 2012, 14(1): 173\u2013185.","journal-title":"Asian Journal of Control"},{"issue":"7","key":"7300_CR11","doi-asserted-by":"publisher","first-page":"1579","DOI":"10.1007\/s11425-009-0114-7","volume":"52","author":"Q X Meng","year":"2009","unstructured":"Meng Q X, A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information, Science in China Series A: Mathematics, 2009, 52(7): 1579\u20131588.","journal-title":"Science in China Series A: Mathematics"},{"issue":"5","key":"7300_CR12","doi-asserted-by":"publisher","first-page":"2945","DOI":"10.1137\/080739781","volume":"48","author":"B \u00d8ksendal","year":"2009","unstructured":"\u00d8ksendal B and Sulem A, Maximum principles for optimal control of forward-backward stochastic differential equations with jumps, SIAM Journal on Control and Optimization, 2009, 48(5): 2945\u20132976.","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"6","key":"7300_CR13","doi-asserted-by":"publisher","first-page":"1230","DOI":"10.1109\/TAC.2009.2019794","volume":"54","author":"G C Wang","year":"2009","unstructured":"Wang G C and Wu Z, The maximum principles for stochastic recursive optimal control problems under partial information, IEEE Transactions on Automatic Control, 2009, 54(6): 1230\u20131242.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"1","key":"7300_CR14","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1137\/110846920","volume":"51","author":"G C Wang","year":"2013","unstructured":"Wang G C, Wu Z, and Xiong J, Maximum principles for forward-backward stochastic control systems with correlated state and observation noises, SIAM Journal on Control and Optimization, 2013, 51(1): 491\u2013524.","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"6","key":"7300_CR15","doi-asserted-by":"publisher","first-page":"2146","DOI":"10.1002\/asjc.1310","volume":"18","author":"H P Ma","year":"2016","unstructured":"Ma H P and Liu B, Linear-quadratic optimal control problem for partially observed forward-backward stochastic differential equations of mean-field type, Asian Journal of Control, 2016, 18(6): 2146\u20132157.","journal-title":"Asian Journal of Control"},{"key":"7300_CR16","doi-asserted-by":"crossref","unstructured":"Wu J B, Wang W C, and Peng Y, Optimal control of fully coupled forward-backward stochastic systems with delay and noisy memory, Proceedings of the 36th Chinese Control Conference (CCC), Dalian, 2017, 1750\u20131755.","DOI":"10.23919\/ChiCC.2017.8027605"},{"key":"7300_CR17","unstructured":"Yong J M and Zhou X Y, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer Science & Business Media, 1999."},{"issue":"2","key":"7300_CR18","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/BF01192514","volume":"98","author":"E Pardoux","year":"1994","unstructured":"Pardoux E and Peng S G, Backward doubly stochastic differential equations and systems of quasilinear spdes, Probability Theory and Related Fields, 1994, 98(2): 209\u2013227.","journal-title":"Probability Theory and Related Fields"},{"issue":"9","key":"7300_CR19","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1016\/S1631-073X(03)00183-3","volume":"336","author":"S G Peng","year":"2003","unstructured":"Peng S G and Shi Y F, A type of time-symmetric forward-backward stochastic differential equations, Comptes Rendus Mathematique, 2003, 336(9): 773\u2013778.","journal-title":"Comptes Rendus Mathematique"},{"issue":"1","key":"7300_CR20","first-page":"73","volume":"24","author":"X J Sun","year":"2008","unstructured":"Sun X J and Lu Y, The property for solutions of the multi-dimensional backward doubly stochastic differential equations with jumps, Chinese Journal of Applied Probability and Statistics, 2008, 24(1): 73\u201382.","journal-title":"Chinese Journal of Applied Probability and Statistics"},{"issue":"7","key":"7300_CR21","doi-asserted-by":"publisher","first-page":"4224","DOI":"10.1137\/080743561","volume":"48","author":"Y C Han","year":"2010","unstructured":"Han Y C, Peng S G, and Wu Z, Maximum principle for backward doubly stochastic control systems with applications, SIAM Journal on Control and Optimization, 2010, 48(7): 4224\u20134241.","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"12","key":"7300_CR22","doi-asserted-by":"publisher","first-page":"1237","DOI":"10.1360\/012013-187","volume":"43","author":"Q F Zhu","year":"2013","unstructured":"Zhu Q F, Wang X, and Shi Y F, Maximum principles for backward doubly stochastic systems with jumps and applications, Scientia Sinica Mathematica, 2013, 43(12): 1237\u20131257.","journal-title":"Scientia Sinica Mathematica"},{"issue":"1","key":"7300_CR23","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1109\/TAC.2014.2322212","volume":"60","author":"Q F Zhu","year":"2015","unstructured":"Zhu Q F and Shi Y F, Optimal control of backward doubly stochastic systems with partial information, IEEE Transactions on Automatic Control, 2015, 60(1): 173\u2013178.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"1","key":"7300_CR24","doi-asserted-by":"publisher","first-page":"215","DOI":"10.22436\/jnsa.010.01.21","volume":"10","author":"J Xu","year":"2017","unstructured":"Xu J and Han Y C, Stochastic maximum principle for delayed backward doubly stochastic control systems, Journal of Nonlinear Sciences & Applications, 2017, 10(1): 215\u2013226.","journal-title":"Journal of Nonlinear Sciences & Applications"},{"issue":"4","key":"7300_CR25","first-page":"1174","volume":"17","author":"L Q Zhang","year":"2011","unstructured":"Zhang L Q and Shi Y F, Maximum principle for forward-backward doubly stochastic control systems and applications, ESAIM: Control, Optimisation and Calculus of Variations, 2011, 17(4): 1174\u20131197.","journal-title":"ESAIM: Control, Optimisation and Calculus of Variations"},{"key":"7300_CR26","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780199219704.001.0001","volume-title":"An Introduction to Stochastic Filtering Theory","author":"J Xiong","year":"2008","unstructured":"Xiong J, An Introduction to Stochastic Filtering Theory, Oxford University Press on Demand, New York, 2008."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-018-7300-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11424-018-7300-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-018-7300-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T22:58:38Z","timestamp":1720911518000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11424-018-7300-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,4]]},"references-count":26,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["7300"],"URL":"https:\/\/doi.org\/10.1007\/s11424-018-7300-z","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,4]]},"assertion":[{"value":"18 September 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 January 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}