{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:35:13Z","timestamp":1787340913474,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM\/ASA J. Uncertainty Quantification"],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>Suppose an approximation to the solution of a backward SDE is precomputed by some numerical algorithm. In this paper we provide a posteriori estimates on the $L^2$-approximation error between true solution and approximate solution. These a posteriori estimates provide upper and lower bounds for the approximation error. They can be expressed solely in terms of the approximate solution and the data of the backward SDE, and can be estimated consistently by simulation in typical situations. We also illustrate by some numerical experiments in the context of least-squares Monte Carlo how the a posteriori estimates can be applied in practice.<\/jats:p>","DOI":"10.1137\/120878689","type":"journal-article","created":{"date-parts":[[2013,5,15]],"date-time":"2013-05-15T11:09:20Z","timestamp":1368616160000},"page":"139-163","source":"Crossref","is-referenced-by-count":16,"title":["A Posteriori Estimates for Backward SDEs"],"prefix":"10.1137","volume":"1","author":[{"given":"Christian","family":"Bender","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jessica","family":"Steiner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,3,27]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1072215199"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.03.005"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"C. Bender and J. Steiner (2012),\n                      Least-squares Monte Carlo for BSDEs\n                      , in Numerical Methods in Finance, R. A. Carmona, P. Del Moral, P. Hu, and N. Oudjane, eds., Springer, Berlin, pp. 257-289.","DOI":"10.1007\/978-3-642-25746-9_8"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1214\/07-AAP448"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(73)90066-8"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2007.03.010"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2004.01.001"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/090765766"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00022"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"C. Geiss, S. Geiss, and E. Gobet (2011),\n                      Fractional smoothness and applications to finance\n                      , in Advanced Mathematical Methods for Finance, G. Di Nunno and B. \u00d8ksendal, eds., Springer, Berlin, pp. 313-332.","DOI":"10.1007\/978-3-642-18412-3_12"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2006.10.007"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2010.03.003"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.3150\/bj\/1161614951"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/14.1.113"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(90)90082-6"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"E. Pardoux and S. G. Peng (1992),\n                      Backward stochastic differential equations and quasilinear parabolic partial differential equations\n                      , in Stochastic Partial Differential Equations and Their Applications, B. L. 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Zhou (1999),\n                      Stochastic Controls: Hamiltonian Systems and HJB Equations\n                      , Springer, Berlin.","DOI":"10.1007\/978-1-4612-1466-3"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1075828058"}],"container-title":["SIAM\/ASA Journal on Uncertainty Quantification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/120878689","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:55:44Z","timestamp":1787338544000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/120878689"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["10.1137\/120878689"],"URL":"https:\/\/doi.org\/10.1137\/120878689","relation":{},"ISSN":["2166-2525"],"issn-type":[{"value":"2166-2525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]}}}