{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:31:41Z","timestamp":1787322701496,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>We consider an optimal stochastic control problem, assuming Lipschitz conditions and allowing degeneracy of the diffusion coefficient, under some structural constraint on the state equation. We formulate the problem in the strong form; i.e., we fix the probability space. We relate the value function and the feedback law to a forward-backward stochastic differential system. We prove existence and uniqueness of a global solution to the latter and deduce existence and, in some cases, uniqueness of an optimal control. To solve the (coupled) forward-backward system we use a priori estimates which follow from its control-theoretic interpretation.<\/jats:p>","DOI":"10.1137\/s0363012903428664","type":"journal-article","created":{"date-parts":[[2004,9,20]],"date-time":"2004-09-20T21:00:29Z","timestamp":1095714029000},"page":"813-830","source":"Crossref","is-referenced-by-count":15,"title":["Existence of Optimal Stochastic Controls and Global Solutions of Forward-Backward Stochastic Differential Equations"],"prefix":"10.1137","volume":"43","author":[{"given":"Marco","family":"Fuhrman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gianmario","family":"Tessitore","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177005363"},{"key":"R2","unstructured":"V. Bally, E. Pardoux, and L. Stoica,\n                      Backward Stochastic Differential Equations Associated to a Symmetric Markov Process\n                      , Tech. rep. 4454, INRIA Rocquencourt, Le Chesnay, France, 2002."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/b80743"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(02)00085-6"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1080\/17442508708833443"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00022"},{"key":"R7","volume-title":"Controlled Markov processes and viscosity solutions","author":"Fleming Wendell","year":"1993"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1080\/17442509408833908"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(98)00038-6"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(94)00011-J"},{"key":"R11","unstructured":"S.Hamadene, J.\u2010P.Lepeltier, S.Peng, BSDEs with continuous coefficients and stochastic differential games, Pitman Res. Notes Math. Ser., Vol. 364, Longman, Harlow, 1997, 115\u20131281752678"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/0328049"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01204218"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(99)00106-4"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Ural\u2019ceva,\n                      Linear and Quasi\u2010Linear Equations of Parabolic Type\n                      , Transl. Math. Monogr. 23, AMS, Providence, RI, 1968.","DOI":"10.1090\/mmono\/023"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01192258"},{"key":"R17","volume-title":"Forward\u2010backward stochastic differential equations and their applications","author":"Ma Jin","year":"1999"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"\u00c9tiennePardoux, Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order, Progr. Probab., Vol. 42, Birkh\u00e4user Boston, Boston, MA, 1998, 79\u201312799m:35279","DOI":"10.1007\/978-1-4612-2022-0_2"},{"key":"R19","doi-asserted-by":"crossref","unstructured":"\u00c9tiennePardoux, BSDEs, weak convergence and homogenization of semilinear PDEs, NATO Sci. Ser. C Math. Phys. Sci., Vol. 528, Kluwer Acad. Publ., Dordrecht, 1999, 503\u20135492000e:60096","DOI":"10.1007\/978-94-011-4560-2_9"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1007\/s004409970001"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996313549"},{"key":"R22","volume-title":"General theory of Markov processes","author":"Sharpe Michael","year":"1988"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1466-3"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012903428664","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:24:30Z","timestamp":1787318670000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012903428664"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1137\/S0363012903428664"],"URL":"https:\/\/doi.org\/10.1137\/s0363012903428664","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]}}}