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Control Optim."],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:p>We prove the existence and uniqueness of solutions to a class of quadratic backward SDE (BSDE) systems which we call triangular quadratic. Our results generalize several existing results about diagonally quadratic BSDEs in the non-Markovian setting. As part of our analysis, we obtain new results about linear BSDEs with unbounded coefficients, which may be of independent interest. Through a nonuniqueness example, we answer a \u201ccrucial open question\u201d raised by Harter and Richou by showing that the stochastic exponential of an $n \\times n$ matrix-valued bounded mean oscillation martingale need not satisfy a reverse H\u00f6lder inequality.<\/jats:p>","DOI":"10.1137\/21m1435689","type":"journal-article","created":{"date-parts":[[2022,6,2]],"date-time":"2022-06-02T11:20:16Z","timestamp":1654168816000},"page":"1642-1666","source":"Crossref","is-referenced-by-count":5,"title":["Existence and Uniqueness for Non-Markovian Triangular Quadratic BSDEs"],"prefix":"10.1137","volume":"60","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6227-2808","authenticated-orcid":true,"given":"Joe","family":"Jackson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gordan","family":"\u017ditkovi\u0107","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,6,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(73)90066-8"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2013.02.013"},{"key":"atypb3","unstructured":"J.F. Chassagneux, S. Nadtochiy, and A. Richou,\n                      Reflected BSDEs in Non-Convex Domains\n                      , preprint, arXiv:2102.06579, 2021,https:\/\/arxiv.org\/abs\/2102.06579."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2015.0721"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176988182"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-008-0191-5"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(03)00059-0"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00022"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"M. Emery,\n                      Stochastic Calculus in Manifolds\n                      , Springer, Berlin, 1989.","DOI":"10.1007\/978-3-642-75051-9"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1111\/mafi.12034"},{"key":"atypb11","unstructured":"S. Fan, Y. Hu, and S. Tang,\n                      Multi-Dimensional Backward Stochastic Differential Equations of Diagonally Quadratic Generators: The General Result\n                      , preprint, arXiv:2007.04481, 2020,https:\/\/arxiv.org\/abs\/2007.04481."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s11579-011-0039-0"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1214\/18-EJP260"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2015.10.011"},{"key":"atypb15","unstructured":"C. Kardaras, H. Xing, and G. \u017ditkovi\u0107,\n                      Incomplete Stochastic Equilibria for Dynamic Monetary Utility\n                      , preprint, arXiv:1505.07224, 2017,https:\/\/arxiv.org\/abs\/1505.07224."},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"N. Kazamaki,\n                      Continuous Exponential Martingales and BMO\n                      , Springer, Berlin, 1994.","DOI":"10.1007\/BFb0073585"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1019160253"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"J. Lee,\n                      Introduction to Riemannian Manifolds\n                      , Springer, Cham, 2018.","DOI":"10.1007\/978-3-319-91755-9"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1214\/20-EJP504"},{"key":"atypb20","unstructured":"K. Nam,\n                      Global Well-Posedness of Non-Markovian Multidimensional Superquadratic BSDE\n                      , preprint, ArXiv:1912.03692, 2019,https:\/\/arxiv.org\/abs\/1912.03692."},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"D. Nualart and E. Nualart,\n                      Introduction to Malliavin Calculus\n                      , Institute of Mathematical Statistics Textbooks, Cambridge University Press, Cambridge, UK, 2018,https:\/\/doi.org\/10.1017\/9781139856485.","DOI":"10.1017\/9781139856485"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(90)90082-6"},{"key":"atypb23","first-page":"265","author":"Peng S.","year":"1999","journal-title":"Boston"},{"key":"atypb24","unstructured":"P. E. Protter,\n                      Stochastic Integration and Differential Equations\n                      , 2nd ed., Stoch. Model. Appl. Probab., Springer, Berlin, 2004."},{"key":"atypb25","first-page":"344","author":"Schachermayer W.","year":"1996","journal-title":"Berlin"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.05.009"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1214\/17-AOP1190"},{"key":"atypb28","doi-asserted-by":"crossref","unstructured":"J. Zhang,\n                      Backward Stochastic Differential Equations\n                      , Springer, New York, 2017.","DOI":"10.1007\/978-1-4939-7256-2"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1435689","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:01:02Z","timestamp":1787320862000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1435689"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["10.1137\/21M1435689"],"URL":"https:\/\/doi.org\/10.1137\/21m1435689","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6]]}}}