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Alanko and M. Avellaneda,\nReducing variance in the numerical solution of BSDEs,\nC. R. Math. Acad. Sci. Paris 351 (2013), no. 3\u20134, 135\u2013138.","DOI":"10.1016\/j.crma.2013.02.010"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_002","unstructured":"V. Bally,\nApproximation scheme for solutions of BSDE,\nBackward Stochastic Differential Equations,\nPitman Res. Notes Math. Ser. 364,\nLongman, Harlow (1997), 177\u2013191."},{"key":"2024052809495383569_j_mcma-2024-2002_ref_003","unstructured":"G. Barles and E. Lesigne,\nSDE, BSDE and PDE,\nBackward Stochastic Differential Equations,\nPitman Res. Notes Math. Ser. 364,\nLongman, Harlow (1997), 47\u201380."},{"key":"2024052809495383569_j_mcma-2024-2002_ref_004","doi-asserted-by":"crossref","unstructured":"O. E. Barndorff-Nielsen,\nAsymptotic techniques; for use in statistics,\nTechnical report, 1989.","DOI":"10.1007\/978-1-4899-3424-6"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_005","doi-asserted-by":"crossref","unstructured":"C. Bender and J. Steiner,\nA posteriori estimates for backward SDEs,\nSIAM\/ASA J. Uncertain. Quantif. 1 (2013), no. 1, 139\u2013163.","DOI":"10.1137\/120878689"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_006","doi-asserted-by":"crossref","unstructured":"J.-M. Bismut,\nConjugate convex functions in optimal stochastic control,\nJ. Math. Anal. Appl. 44 (1973), 384\u2013404.","DOI":"10.1016\/0022-247X(73)90066-8"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_007","doi-asserted-by":"crossref","unstructured":"B. Bouchard and N. Touzi,\nDiscrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations,\nStochastic Process. Appl. 111 (2004), no. 2, 175\u2013206.","DOI":"10.1016\/j.spa.2004.01.001"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_008","doi-asserted-by":"crossref","unstructured":"P. Briand and C. Labart,\nSimulation of BSDEs by Wiener chaos expansion,\nAnn. Appl. Probab. 24 (2014), no. 3, 1129\u20131171.","DOI":"10.1214\/13-AAP943"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_009","doi-asserted-by":"crossref","unstructured":"J. M. Burgers,\nA mathematical model illustrating the theory of turbulence,\nAdvances in Applied Mechanics,\nAcademic Press, New York (1948), 171\u2013199.","DOI":"10.1016\/S0065-2156(08)70100-5"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_010","doi-asserted-by":"crossref","unstructured":"J.-F. Chassagneux and C. A. Garcia Trillos,\nCubature method to solve BSDEs: Error expansion and complexity control,\nMath. Comp. 89 (2020), no. 324, 1895\u20131932.","DOI":"10.1090\/mcom\/3522"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_011","doi-asserted-by":"crossref","unstructured":"J.-F. Chassagneux and A. Richou,\nNumerical simulation of quadratic BSDEs,\nAnn. Appl. Probab. 26 (2016), no. 1, 262\u2013304.","DOI":"10.1214\/14-AAP1090"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_012","doi-asserted-by":"crossref","unstructured":"P. E. Chaudru de Raynal and C. A. Garcia Trillos,\nA cubature based algorithm to solve decoupled McKean\u2013Vlasov forward-backward stochastic differential equations,\nStochastic Process. Appl. 125 (2015), no. 6, 2206\u20132255.","DOI":"10.1016\/j.spa.2014.11.018"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_013","doi-asserted-by":"crossref","unstructured":"P. Cheridito, H. M. Soner, N. Touzi and N. Victoir,\nSecond-order backward stochastic differential equations and fully nonlinear parabolic PDEs,\nComm. Pure Appl. Math. 60 (2007), no. 7, 1081\u20131110.","DOI":"10.1002\/cpa.20168"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_014","doi-asserted-by":"crossref","unstructured":"P. Cheridito and M. Stadje,\nBS\u0394Es and BSDEs with non-Lipschitz drivers: Comparison, convergence and robustness,\nBernoulli 19 (2013), no. 3, 1047\u20131085.","DOI":"10.3150\/12-BEJ445"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_015","unstructured":"D. Chevance,\nR\u00e9solution num\u00e9rique des \u00e9quations diff\u00e9rentielles stochastiques r\u00e9trogrades,\nPhD thesis, Universtit\u00e9 de Provence, 1997."},{"key":"2024052809495383569_j_mcma-2024-2002_ref_016","doi-asserted-by":"crossref","unstructured":"D. Crisan and K. Manolarakis,\nSolving backward stochastic differential equations using the cubature method: Application to nonlinear pricing,\nSIAM J. 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El Karoui, S. Hamad\u00e8ne and A. Matoussi,\nBackward stochastic differential equations and applications,\nIndifference Pricing Theory Appl. 8 (2008), 267\u2013320.","DOI":"10.1515\/9781400833115.267"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_024","doi-asserted-by":"crossref","unstructured":"N. El Karoui, S. Peng and M. C. Quenez,\nBackward stochastic differential equations in finance,\nMath. Finance 7 (1997), no. 1, 1\u201371.","DOI":"10.1111\/1467-9965.00022"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_025","doi-asserted-by":"crossref","unstructured":"M. Fujii, A. Takahashi and M. Takahashi,\nAsymptotic expansion as prior knowledge in deep learning method for high dimensional BSDES,\nAsia-Pacific Financial Markets 26 (2019), no. 3, 391\u2013408.","DOI":"10.1007\/s10690-019-09271-7"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_026","doi-asserted-by":"crossref","unstructured":"H. Geman, N. El Karoui and J.-C. Rochet,\nChanges of num\u00e9raire, changes of probability measure and option pricing,\nJ. Appl. Probab. 32 (1995), no. 2, 443\u2013458.","DOI":"10.2307\/3215299"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_027","doi-asserted-by":"crossref","unstructured":"M. Germain, H. Pham and X. Warin,\nApproximation error analysis of some deep backward schemes for nonlinear PDEs,\nSIAM J. Sci. Comput. 44 (2022), no. 1, 28\u201356.","DOI":"10.1137\/20M1355355"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_028","doi-asserted-by":"crossref","unstructured":"O. Glass and S. Guerrero,\nOn the uniform controllability of the Burgers equation,\nSIAM J. Control Optim. 46 (2007), no. 4, 1211\u20131238.","DOI":"10.1137\/060664677"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_029","doi-asserted-by":"crossref","unstructured":"P. Glasserman and B. 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Appl. 117 (2007), no. 7, 803\u2013829.","DOI":"10.1016\/j.spa.2006.10.007"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_033","doi-asserted-by":"crossref","unstructured":"E. Gobet, J.-P. Lemor and X. Warin,\nA regression-based Monte Carlo method to solve backward stochastic differential equations,\nAnn. Appl. Probab. 15 (2005), no. 3, 2172\u20132202.","DOI":"10.1214\/105051605000000412"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_034","doi-asserted-by":"crossref","unstructured":"E. Gobet and P. Turkedjiev,\nApproximation of backward stochastic differential equations using Malliavin weights and least-squares regression,\nBernoulli 22 (2016), no. 1, 530\u2013562.","DOI":"10.3150\/14-BEJ667"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_035","doi-asserted-by":"crossref","unstructured":"B. Gong and H. Rui,\nOne order numerical scheme for forward-backward stochastic differential equations,\nAppl. Math. Comput. 271 (2015), 220\u2013231.","DOI":"10.1016\/j.amc.2015.08.127"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_036","doi-asserted-by":"crossref","unstructured":"S. Hamad\u00e8ne and M. Jeanblanc,\nOn the starting and stopping problem: Application in reversible investments,\nMath. Oper. Res. 32 (2007), no. 1, 182\u2013192.","DOI":"10.1287\/moor.1060.0228"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_037","doi-asserted-by":"crossref","unstructured":"J. Han and J. Long,\nConvergence of the deep BSDE method for coupled FBSDEs,\nProbab. Uncertain. Quant. Risk 5 (2020), Paper No. 5.","DOI":"10.1186\/s41546-020-00047-w"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_038","doi-asserted-by":"crossref","unstructured":"B. Holmquist,\nThe \ud835\udc51-variate vector Hermite polynomial of order \ud835\udc58,\nLinear Algebra Appl. 237 (1996), 155\u2013190.","DOI":"10.1016\/0024-3795(95)00595-1"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_039","doi-asserted-by":"crossref","unstructured":"Y. Hu, P. Imkeller and M. M\u00fcller,\nUtility maximization in incomplete markets,\nAnn. Appl. Probab. 15 (2005), no. 3, 1691\u20131712.","DOI":"10.1214\/105051605000000188"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_040","doi-asserted-by":"crossref","unstructured":"T. P. Huijskens, M. J. Ruijter and C. W. Oosterlee,\nEfficient numerical Fourier methods for coupled forward-backward SDEs,\nJ. Comput. Appl. Math. 296 (2016), 593\u2013612.","DOI":"10.1016\/j.cam.2015.10.019"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_041","doi-asserted-by":"crossref","unstructured":"C. Hur\u00e9, H. Pham and X. Warin,\nDeep backward schemes for high-dimensional nonlinear PDEs,\nMath. Comp. 89 (2020), no. 324, 1547\u20131579.","DOI":"10.1090\/mcom\/3514"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_042","unstructured":"M. Hutzenthaler, A. Jentzen, T. Kruse and T. A. Nguyen,\nOvercoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations,\nJ. Numer. Math. 31 (2023), no. 1, 1\u201328."},{"key":"2024052809495383569_j_mcma-2024-2002_ref_043","doi-asserted-by":"crossref","unstructured":"M. Hutzenthaler, T. Kruse and T. A. Nguyen,\nOn the speed of convergence of Picard iterations of backward stochastic differential equations,\nProbab. Uncertain. Quant. Risk 7 (2022), no. 2, 133\u2013150.","DOI":"10.3934\/puqr.2022009"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_044","unstructured":"C. B. Hyndman and P. O. Ngou,\nGlobal convergence and stability of a convolution method for numerical solution of bsdes, preprint (2014), https:\/\/arxiv.org\/abs\/1410.8595."},{"key":"2024052809495383569_j_mcma-2024-2002_ref_045","doi-asserted-by":"crossref","unstructured":"A. Khedher and M. Vanmaele,\nDiscretisation of FBSDEs driven by c\u00e0dl\u00e0g martingales,\nJ. Math. Anal. Appl. 435 (2016), no. 1, 508\u2013531.","DOI":"10.1016\/j.jmaa.2015.10.022"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_046","doi-asserted-by":"crossref","unstructured":"T. Kollo and D. von Rosen,\nAdvanced Multivariate Statistics with Matrices,\nMath. Appl. (New York) 579,\nSpringer, Dordrecht, 2005.","DOI":"10.1007\/1-4020-3419-9"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_047","doi-asserted-by":"crossref","unstructured":"R. J. A. Laeven and M. Stadje,\nRobust portfolio choice and indifference valuation,\nMath. Oper. 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Rev. 88 (1998), no. 3, 323\u2013349."},{"key":"2024052809495383569_j_mcma-2024-2002_ref_051","doi-asserted-by":"crossref","unstructured":"T. M\u00f8ller,\nOn valuation and risk management at the interface of insurance and finance,\nBritish Actuarial J. 8 (2002), no. 4, 787\u2013827.","DOI":"10.1017\/S1357321700003913"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_052","doi-asserted-by":"crossref","unstructured":"E. Pardoux and S. Peng,\nAdapted solution of a backward stochastic differential equation,\nSystems Control Lett. 14 (1990), no. 1, 55\u201361.","DOI":"10.1016\/0167-6911(90)90082-6"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_053","doi-asserted-by":"crossref","unstructured":"E. Pardoux and S. Peng,\nBackward stochastic differential equations and quasilinear parabolic partial differential equations,\nStochastic Partial Differential Equations and Their Applications,\nLect. Notes Control Inf. Sci. 176,\nSpringer, Berlin (1992), 200\u2013217.","DOI":"10.1007\/BFb0007334"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_054","doi-asserted-by":"crossref","unstructured":"A. Pelsser and K. Gnameho,\nA Monte Carlo method for backward stochastic differential equations with Hermite martingales,\nMonte Carlo Methods Appl. 25 (2019), no. 1, 37\u201360.","DOI":"10.1515\/mcma-2019-2028"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_055","doi-asserted-by":"crossref","unstructured":"B. Ribeiro, R. F. Albrecht, A. Dobnikar, D. W. Pearson and N. C. Steele,\nAdaptive and Natural Computing Algorithms,\nSpringer, Vienna, 2005.","DOI":"10.1007\/b138998"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_056","doi-asserted-by":"crossref","unstructured":"L. Stentoft,\nConvergence of the least squares Monte Carlo approach to American option valuation,\nManag. Sci. 50 (2004), no. 9, 1193\u20131203.","DOI":"10.1287\/mnsc.1030.0155"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_057","doi-asserted-by":"crossref","unstructured":"B. Sudret,\nGlobal sensitivity analysis using polynomial chaos expansions,\nReliab. Eng. Syst. Safety 93 (2008), no. 7, 964\u2013979.","DOI":"10.1016\/j.ress.2007.04.002"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_058","doi-asserted-by":"crossref","unstructured":"W. A. Ventura and A. Korzeniowski,\nOn discretely reflected backward stochastic differential equations,\nStoch. Anal. Appl. 34 (2016), no. 1, 1\u201323.","DOI":"10.1080\/07362994.2015.1094670"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_059","doi-asserted-by":"crossref","unstructured":"C. S. Withers,\nA simple expression for the multivariate Hermite polynomials,\nStatist. Probab. Lett. 47 (2000), no. 2, 165\u2013169.","DOI":"10.1016\/S0167-7152(99)00153-4"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_060","doi-asserted-by":"crossref","unstructured":"M. V. W\u00fcthrich and M. Merz,\nFinancial Modeling, Actuarial Valuation and Solvency in Insurance,\nSpringer Finance,\nSpringer, Heidelberg, 2013.","DOI":"10.1007\/978-3-642-31392-9"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_061","doi-asserted-by":"crossref","unstructured":"D. Xiu and G. E. Karniadakis,\nModeling uncertainty in flow simulations via generalized polynomial chaos,\nJ. Comput. Phys. 187 (2003), no. 1, 137\u2013167.","DOI":"10.1016\/S0021-9991(03)00092-5"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_062","doi-asserted-by":"crossref","unstructured":"J. Zhang,\nA numerical scheme for BSDEs,\nAnn. Appl. Probab. 14 (2004), no. 1, 459\u2013488.","DOI":"10.1214\/aoap\/1075828058"},{"key":"2024052809495383569_j_mcma-2024-2002_ref_063","doi-asserted-by":"crossref","unstructured":"W. Zhao, L. Chen and S. Peng,\nA new kind of accurate numerical method for backward stochastic differential equations,\nSIAM J. Sci. 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