{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:55Z","timestamp":1787337295546,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>In this paper, we propose a new kind of numerical simulation method for backward stochastic differential equations (BSDEs). We discretize the continuous BSDEs on time\u2010space discrete grids, use the Monte Carlo method to approximate mathematical expectations, and use space interpolations to compute values at non\u2010grid points. To demonstrate the accuracy and the effectiveness of our method, several numerical examples are given.<\/jats:p>","DOI":"10.1137\/05063341x","type":"journal-article","created":{"date-parts":[[2006,9,21]],"date-time":"2006-09-21T18:09:08Z","timestamp":1158862148000},"page":"1563-1581","source":"Crossref","is-referenced-by-count":102,"title":["A New Kind of Accurate Numerical Method for Backward Stochastic Differential Equations"],"prefix":"10.1137","volume":"28","author":[{"given":"Weidong","family":"Zhao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lifeng","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shige","family":"Peng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,9,15]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1080\/07362990008809652"},{"key":"R2","unstructured":"V. Bally,\n                      An approximation scheme for BSDEs and applications to control and nonlinear PDEs\n                      , Pitman Research Notes in Mathematics Series, Longman, 364 (1997)."},{"key":"R3","first-page":"1","volume":"6","author":"Bally V.","year":"2003","journal-title":"Bernoulli","ISSN":"https:\/\/id.crossref.org\/issn\/1350-7265","issn-type":"print"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(03)00026-7"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF00052324"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2004.01.001"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706645"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"J . C. Butcher,\n                      Numerical Methods for Ordinary Differential Equations\n                      , John wiley & Sons, 2003.","DOI":"10.1002\/0470868279"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"D. Chevance,\n                      Numerical Methods for Backward Stochastic Differential Equations\n                      , in Numerical Methods in Finance, Edt L. C. G. Rogers and D. Talay, Cambridge University Press, 1997, pp. 232\u2013244.","DOI":"10.1017\/CBO9781139173056.013"},{"key":"R10","unstructured":"G. C. Chow,\n                      Dynamic Economics: Optimization by the Lagrange Method\n                      , Oxford University Press, 1997."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(98)00013-1"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1034968235"},{"key":"R13","unstructured":"L. C. Evans,\n                      Partial Differential Equations\n                      , American Mathematical Society, 2002."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/PL00013529"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/s007800050068"},{"key":"R16","unstructured":"N. Ikeda and S. Watanabe,\n                      Stochastic Differential Equations and Diffusion Processes\n                      , North\u2010Holland Publishing Company, Amsterdam$\\cdot$Oxford$\\cdot$New York, Kodansha LTD, 1981."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1024404416"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00022"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/s00032-002-0006-6"},{"key":"R20","unstructured":"P. E. Kloeden and E. Platen,\n                      Numerical Solution of Stochastic Differential Equations\n                      , Springer\u2010Verlag, Berlin, Third Printing, 1999."},{"key":"R21","unstructured":"P. E. Kloeden, E. Platen, and H. Schurz,\n                      Numerical Solution of SDE Through Computer Experiments\n                      , Springer\u2010Verlag, Berlin, Second Printing, 1997."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/14.1.113"},{"key":"R23","first-page":"302","volume":"12","author":"Ma J.","year":"2000","journal-title":"Annals of Applied Probability","ISSN":"https:\/\/id.crossref.org\/issn\/1050-5164","issn-type":"print"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01192258"},{"key":"R25","unstructured":"J. Ma and J. Yong,\n                      Forward\u2010Backward Stochastic Differential Equations and Their Applications\n                      , Lecture Notes in Math., 1702, Springer, 1999."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(90)90082-6"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/0328054"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1080\/17442509108833727"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1080\/17442509208833749"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0106.00079"},{"key":"R31","doi-asserted-by":"crossref","unstructured":"G. Da Prato and J. Zabczyk,\n                      Second Order Partial Differential Equations in Hilbert Spaces\n                      , Cambridge University Press, 2002.","DOI":"10.1017\/CBO9780511543210"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1142\/S0219493701000035"},{"key":"R33","unstructured":"J. Zhang,\n                      Some Fine Properties of Backward Stochastic Differential Equations\n                      , Ph.D. Thesis, Purdue University, 2001."},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1075828058"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1155\/S0161171202110234"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/05063341X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:55:00Z","timestamp":1787334900000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/05063341X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":35,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/05063341X"],"URL":"https:\/\/doi.org\/10.1137\/05063341x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}