{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T03:28:03Z","timestamp":1671593283561},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2017,9,9]],"date-time":"2017-09-09T00:00:00Z","timestamp":1504915200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Research Grant from University of Macau","award":["MYRG068(Y1-L2)-FST13-DD"],"award-info":[{"award-number":["MYRG068(Y1-L2)-FST13-DD"]}]},{"name":"Science and Technology Development Fund, Macao S.A.R. FDCT","award":["081\/2016\/A2"],"award-info":[{"award-number":["081\/2016\/A2"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1007\/s00180-017-0763-x","type":"journal-article","created":{"date-parts":[[2017,9,11]],"date-time":"2017-09-11T16:09:55Z","timestamp":1505146195000},"page":"1357-1373","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A regression-based numerical scheme for backward stochastic differential equations"],"prefix":"10.1007","volume":"32","author":[{"given":"Deng","family":"Ding","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofei","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiqi","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,9,9]]},"reference":[{"key":"763_CR1","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1214\/aoap\/1177005363","volume":"3","author":"F Antonelli","year":"1993","unstructured":"Antonelli F (1993) Backward\u2013forward stochastic differential equations. Ann Appl Probab 3:777\u2013793","journal-title":"Ann Appl Probab"},{"key":"763_CR2","volume-title":"Approximation scheme for solutions of BSDE. Pitman research notes in mathematics series","author":"V Bally","year":"1997","unstructured":"Bally V (1997) Approximation scheme for solutions of BSDE. Pitman research notes in mathematics series. Longman, Harlow"},{"key":"763_CR3","doi-asserted-by":"crossref","unstructured":"Bender C, Steiner J (2012) Least-squares Monte Carlo for backward SDEs. In: Carmona RA et al (eds) Numerical methods in finance. Springer, Berlin","DOI":"10.1007\/978-3-642-25746-9_8"},{"key":"763_CR4","volume-title":"Advanced mathematical methods for scientists and engineers. International series in pure and applied mathematics","author":"CM Bender","year":"1978","unstructured":"Bender CM, Orszag SA (1978) Advanced mathematical methods for scientists and engineers. International series in pure and applied mathematics. McGraw-Hill Book Co, New York"},{"issue":"2","key":"763_CR5","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/0022-247X(73)90066-8","volume":"44","author":"JM Bismut","year":"1973","unstructured":"Bismut JM (1973) Conjugate convex functions in optimal stochastic control. J Math Anal Appl 44(2):384\u2013404","journal-title":"J Math Anal Appl"},{"issue":"2","key":"763_CR6","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.spa.2004.01.001","volume":"111","author":"B Bouchaud","year":"2004","unstructured":"Bouchaud B, Touzi N (2004) Discrete time approximation and Monte Carlo simulation of backward stochastic differential equations. Stoch Process Appl 111(2):175\u2013206","journal-title":"Stoch Process Appl"},{"key":"763_CR7","volume-title":"Chebyshev and Fourier spectral methods","author":"JP Boyd","year":"2001","unstructured":"Boyd JP (2001) Chebyshev and Fourier spectral methods, 2nd edn. Dover Publications Inc, Mineola","edition":"2"},{"issue":"2","key":"763_CR8","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1137\/080718061","volume":"31","author":"F Fang","year":"2008","unstructured":"Fang F, Oosterlee CW (2008) A novel pricing method for European options based on Fourier-cosine series expansions. SIAM J Sci Comput 31(2):826\u2013848","journal-title":"SIAM J Sci Comput"},{"issue":"3","key":"763_CR9","doi-asserted-by":"crossref","first-page":"2172","DOI":"10.1214\/105051605000000412","volume":"15","author":"E Gobet","year":"2005","unstructured":"Gobet E, Lemor JP, Warin X (2005) A regression-based Monte Carlo method to solve backward stochastic differential equations. Ann Appl Probab 15(3):2172\u20132202","journal-title":"Ann Appl Probab"},{"key":"763_CR10","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.cam.2015.10.019","volume":"296","author":"TP Huijskens","year":"2016","unstructured":"Huijskens TP, Ruijter MJ, Oosterlee CW (2016) Efficient numerical Fourier methods for coupled forward\u2013backward SDEs. J Comput Appl Math 296:593\u2013612","journal-title":"J Comput Appl Math"},{"issue":"5","key":"763_CR11","doi-asserted-by":"crossref","first-page":"889","DOI":"10.3150\/bj\/1161614951","volume":"12","author":"JP Lemor","year":"2006","unstructured":"Lemor JP, Gobet E, Warin X (2006) Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations. Bernoulli 12(5):889\u2013916","journal-title":"Bernoulli"},{"issue":"3","key":"763_CR12","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/BF01192258","volume":"98","author":"J Ma","year":"1994","unstructured":"Ma J, Protter P, Yong JM (1994) Solving forward\u2013backward stochastic differential equations explicitly: a four step scheme. Probab Theory Related Fields 98(3):339\u2013359","journal-title":"Probab Theory Related Fields"},{"issue":"1","key":"763_CR13","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/0167-6911(90)90082-6","volume":"14","author":"E Pardoux","year":"1990","unstructured":"Pardoux E, Peng SG (1990) Adapted solution of a backward stochastic differential equation. Syst Control Lett 14(1):55\u201361","journal-title":"Syst Control Lett"},{"key":"763_CR14","doi-asserted-by":"crossref","unstructured":"Pardoux E, Peng SG (1992) Backward stochastic differential equations and quasilinear parabolic partial differential equations. In: Stochastic partial differential equations and their applications (Charlotte, NC, 1991). Lecture notes control and information sciences, vol 176. Springer, Berlin, pp 200\u2013217","DOI":"10.1007\/BFb0007334"},{"issue":"2","key":"763_CR15","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s40306-015-0128-x","volume":"40","author":"H Pham","year":"2015","unstructured":"Pham H (2015) Feynman\u2013Kac representation of fully nonlinear PDEs and applications. Acta Math Vietnam 40(2):255\u2013269","journal-title":"Acta Math Vietnam"},{"issue":"2","key":"763_CR16","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1137\/130913183","volume":"37","author":"MJ Ruijter","year":"2015","unstructured":"Ruijter MJ, Oosterlee CW (2015) A Fourier cosine method for an efficient computation of solutions to BSDEs. SIAM J Sci Comput 37(2):859\u2013889","journal-title":"SIAM J Sci Comput"},{"key":"763_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apnum.2015.12.003","volume":"103","author":"MJ Ruijter","year":"2016","unstructured":"Ruijter MJ, Oosterlee CW (2016) Numerical Fourier method and second-order Taylor scheme for backward SDEs in finance. Appl Numer Math 103:1\u201326","journal-title":"Appl Numer Math"},{"issue":"1","key":"763_CR18","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1214\/aoap\/1075828058","volume":"14","author":"J Zhang","year":"2004","unstructured":"Zhang J (2004) A numerical scheme for BSDEs. Ann Appl Probab 14(1):459\u2013488","journal-title":"Ann Appl Probab"},{"issue":"4","key":"763_CR19","doi-asserted-by":"crossref","first-page":"1563","DOI":"10.1137\/05063341X","volume":"28","author":"W Zhao","year":"2006","unstructured":"Zhao W, Chen L, Peng SG (2006) A new kind of accurate numerical method for backward stochastic differential equations. SIAM J Sci Comput 28(4):1563\u20131581","journal-title":"SIAM J Sci Comput"},{"issue":"4","key":"763_CR20","doi-asserted-by":"crossref","first-page":"905","DOI":"10.3934\/dcdsb.2009.12.905","volume":"12","author":"W Zhao","year":"2009","unstructured":"Zhao W, Wang J, Peng SG (2009) Error estimates of the theta-scheme for backward stochastic differential equations. Discrete Contin Dyn Syst Ser B 12(4):905\u2013924","journal-title":"Discrete Contin Dyn Syst Ser B"},{"issue":"3","key":"763_CR21","doi-asserted-by":"crossref","first-page":"618","DOI":"10.4208\/cicp.280113.190813a","volume":"15","author":"W Zhao","year":"2014","unstructured":"Zhao W, Zhang W, Ju L (2014) A numerical method and its error estimates for the decoupled forward\u2013backward stochastic differential equations. Commun Comput Phys 15(3):618\u2013646","journal-title":"Commun Comput Phys"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00180-017-0763-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-017-0763-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-017-0763-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,10,14]],"date-time":"2017-10-14T09:07:44Z","timestamp":1507972064000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00180-017-0763-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,9]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["763"],"URL":"https:\/\/doi.org\/10.1007\/s00180-017-0763-x","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,9]]}}}