{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:26:43Z","timestamp":1787318803995,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We present various versions of the maximum principle for optimal control of forward-backward stochastic differential equations (SDE) with jumps. Our study is motivated by risk minimization via g-expectations. We first prove a general sufficient maximum principle for optimal control with partial information of a stochastic system consisting of a forward and a backward SDE driven by L\u00e9vy processes. We then present a Malliavin calculus approach which allows us to handle non\u2013Markovian systems. Finally, we give examples of applications.<\/jats:p>","DOI":"10.1137\/080739781","type":"journal-article","created":{"date-parts":[[2009,11,11]],"date-time":"2009-11-11T18:31:07Z","timestamp":1257964267000},"page":"2945-2976","source":"Crossref","is-referenced-by-count":80,"title":["Maximum Principles for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps"],"prefix":"10.1137","volume":"48","author":[{"given":"Bernt","family":"\u00d8ksendal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Agn\u00e8s","family":"Sulem","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,11,11]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"D. Applebaum,\n                      L\u00e9vy Processes and Stochastic Calculus\n                      , Cambridge University Press, Cambridge, MA, 2004.","DOI":"10.1017\/CBO9780511755323"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1080\/07362990701283128"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"S. Bahlali,\n                      Necessary and sufficient optimality conditions for relaxed and strict control problems of forward-backward systems\n                      , Manuscript, 2008.","DOI":"10.1137\/070681053"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"P. Barrieu and N. El Karoui,\n                      Optimal derivatives design under dynamic risk measures\n                      , Mathematics of Finance, Contemporary Mathematics (A.M.S. Proceedings), (2004), pp. 13\u201326.","DOI":"10.1090\/conm\/351\/06389"},{"key":"R5","unstructured":"S. Biagini and M. Frittelli,\n                      On the extension of the Namioka-Klee theorem and on the Fatou property for risk measures\n                      , Manuscript, 2007."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s004400100172"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"G. Di Nunno, B. \u00d8ksendal, and F. Proske,\n                      Malliavin Calculus for L\u00e9vy Processes with Applications to Finance\n                      , Springer-Verlag, Berlin, 2009.","DOI":"10.1007\/978-3-540-78572-9"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00022"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOTA.0000026132.62934.96"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4266(02)00270-4"},{"key":"R11","first-page":"227","author":"Frittelli M.","year":"2004","journal-title":"In G. Szeg\u00f6 ed., Risk Measures in the 21st Century, John Wiley & Sons, Hoboken"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/s007800200072"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/s007800200069"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1080\/17442509108833682"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1080\/17442500701655408"},{"key":"R16","unstructured":"T. Meyer-Brandis, B. \u00d8ksendal, and X. Y. Zhou,\n                      A stochastic maximum principle via Malliavin calculus\n                      , Eprint, University of Oslo, 10\/2008."},{"key":"R17","unstructured":"Y. Y. Okur,\n                      White noise generalization of the Clark-Ocone formula under change of measure\n                      , Eprint, University of Oslo, 15\/2007."},{"key":"R18","unstructured":"B. \u00d8ksendal and A. Sulem,\n                      Risk indifference pricing in jump diffusion markets\n                      , Math. Finance, (to appear)."},{"key":"R19","doi-asserted-by":"crossref","unstructured":"B. \u00d8ksendal and A. Sulem,\n                      Applied Stochastic Control of Jump Diffusions\n                      , 2nd ed., Springer-Verlag, Berlin, 2007.","DOI":"10.1007\/978-3-540-69826-5"},{"key":"R20","first-page":"141","volume":"364","author":"Peng S.","year":"1997","journal-title":"in N. El Karoui and L. Mazliak eds., Backward Stochastic Differential Equations, Pitman Research Notes in Mathematics Series"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"E. Pardoux\n                      Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order\n                      , in L. Decreusefond et al. eds. Stochastic Analysis and related Topics VI, The Geilo Workshop, 1996, Birkh\u00e4user 1998, pp. 79\u2013127.","DOI":"10.1007\/978-1-4612-2022-0_2"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996313549"},{"key":"R23","doi-asserted-by":"crossref","unstructured":"E. Rosazza Gianin,\n                      \n                        Risk measures via\n                        g\n                        -expectations\n                      \n                      , Insurance: Mathematics and Economics 39 (2006), pp. 19\u201334.","DOI":"10.1016\/j.insmatheco.2006.01.002"},{"key":"R24","unstructured":"J. Shi and Z. Wu,\n                      Maximum principle for fully coupled stochastic control system with random jumps\n                      , in Proceedings of the 26th Chinese Control Conference, Zhangjiajie, Hunan, China, 2007, pp. 375\u2013380."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080739781","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:40:19Z","timestamp":1787316019000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080739781"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,11]]},"references-count":24,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080739781"],"URL":"https:\/\/doi.org\/10.1137\/080739781","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,11]]}}}