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Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations

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Cited by:

  1. Richter, Anja, 2014. "Explicit solutions to quadratic BSDEs and applications to utility maximization in multivariate affine stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3578-3611.
  2. Abbas-Turki Lokman A. & Bouselmi Aych I. & Mikou Mohammed A., 2014. "Toward a coherent Monte Carlo simulation of CVA," Monte Carlo Methods and Applications, De Gruyter, vol. 20(3), pages 195-216, September.
  3. Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2014. "A numerical algorithm for a class of BSDEs via the branching process," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1112-1140.
  4. Bouchard, Bruno & Chassagneux, Jean-François, 2008. "Discrete-time approximation for continuously and discretely reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2269-2293, December.
  5. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
  6. Bouchard Bruno & Tan Xiaolu & Zou Yiyi & Warin Xavier, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.
  7. Ren, Zhenjie & Tan, Xiaolu, 2017. "On the convergence of monotone schemes for path-dependent PDEs," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1738-1762.
  8. Monique Jeanblanc & Thibaut Mastrolia & Dylan Possamaï & Anthony Réveillac, 2015. "Utility Maximization With Random Horizon: A Bsde Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-43, November.
  9. Samuel N. Cohen & Martin Tegn'er, 2018. "European Option Pricing with Stochastic Volatility models under Parameter Uncertainty," Papers 1807.03882, arXiv.org.
  10. Geiss, Christel & Labart, Céline, 2016. "Simulation of BSDEs with jumps by Wiener Chaos expansion," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2123-2162.
  11. Gobet, Emmanuel & Makhlouf, Azmi, 2010. "-time regularity of BSDEs with irregular terminal functions," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1105-1132, July.
  12. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2020. "An implicit numerical scheme for a class of backward doubly stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3295-3324.
  13. Brigo, Damiano & Francischello, Marco & Pallavicini, Andrea, 2019. "Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement," European Journal of Operational Research, Elsevier, vol. 274(2), pages 788-805.
  14. Masaaki Fujii & Akihiko Takahashi, 2015. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(3), pages 283-304, September.
  15. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs with Jumps," CIRJE F-Series CIRJE-F-993, CIRJE, Faculty of Economics, University of Tokyo.
  16. Masaaki Fujii & Akihiko Takahshi, 2015. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," CIRJE F-Series CIRJE-F-954, CIRJE, Faculty of Economics, University of Tokyo.
  17. Ki Wai Chau & Cornelis W. Oosterlee, 2016. "On the wavelets-based SWIFT method for backward stochastic differential equations," Papers 1611.06098, arXiv.org.
  18. Christophette Blanchet-Scalliet & Etienne Chevalier & Idris Kharroubi & Thomas Lim, 2015. "Max–Min Optimization Problem For Variable Annuities Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-35, December.
  19. Jean-Franc{c}ois Chassagneux & Junchao Chen & Noufel Frikha, 2022. "Deep Runge-Kutta schemes for BSDEs," Papers 2212.14372, arXiv.org.
  20. Gobet, Emmanuel & Labart, Céline, 2007. "Error expansion for the discretization of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 803-829, July.
  21. Giorgia Callegaro & Alessandro Gnoatto & Martino Grasselli, 2021. "A Fully Quantization-based Scheme for FBSDEs," Working Papers 07/2021, University of Verona, Department of Economics.
  22. Marie Bernhart & Huyên Pham & Peter Tankov & Xavier Warin, 2011. "Swing Options Valuation:a BSDE with Constrained Jumps Approach," Working Papers hal-00553356, HAL.
  23. Lorenc Kapllani & Long Teng, 2020. "Deep learning algorithms for solving high dimensional nonlinear backward stochastic differential equations," Papers 2010.01319, arXiv.org, revised Jun 2022.
  24. Jean-Franc{c}ois Chassagneux & Mohan Yang, 2021. "Numerical approximation of singular Forward-Backward SDEs," Papers 2106.15496, arXiv.org.
  25. Kraft, Holger & Seifried, Frank Thomas, 2014. "Stochastic differential utility as the continuous-time limit of recursive utility," Journal of Economic Theory, Elsevier, vol. 151(C), pages 528-550.
  26. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs," CARF F-Series CARF-F-372, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  27. Guangbao Guo, 2018. "Finite Difference Methods for the BSDEs in Finance," IJFS, MDPI, vol. 6(1), pages 1-15, March.
  28. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CIRJE F-Series CIRJE-F-1069, CIRJE, Faculty of Economics, University of Tokyo.
  29. Geiss, Christel & Geiss, Stefan & Gobet, Emmanuel, 2012. "Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2078-2116.
  30. Agarwal, Ankush & Claisse, Julien, 2020. "Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5006-5036.
  31. Christian Bender & Nikolaus Schweizer & Jia Zhuo, 2013. "A primal-dual algorithm for BSDEs," Papers 1310.3694, arXiv.org, revised Sep 2014.
  32. Crisan, D. & Manolarakis, K. & Touzi, N., 2010. "On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1133-1158, July.
  33. Andrew Lesniewski, 2020. "Epidemic control via stochastic optimal control," Papers 2004.06680, arXiv.org, revised May 2020.
  34. Andrzej Ruszczynski & Jianing Yao, 2017. "A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation," Papers 1701.06234, arXiv.org, revised Aug 2020.
  35. Giovanni Mottola, 2014. "Reflected Backward SDE approach to the price-hedge of defaultable claims with contingent switching CSA," Papers 1412.1325, arXiv.org, revised Feb 2015.
  36. Bender, Christian & Denk, Robert, 2007. "A forward scheme for backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1793-1812, December.
  37. Polynice Oyono Ngou & Cody Hyndman, 2014. "A Fourier interpolation method for numerical solution of FBSDEs: Global convergence, stability, and higher order discretizations," Papers 1410.8595, arXiv.org, revised May 2022.
  38. Aur'elien Alfonsi & Bernard Lapeyre & J'er^ome Lelong, 2022. "How many inner simulations to compute conditional expectations with least-square Monte Carlo?," Papers 2209.04153, arXiv.org, revised May 2023.
  39. Le Cavil Anthony & Oudjane Nadia & Russo Francesco, 2018. "Monte-Carlo algorithms for a forward Feynman–Kac-type representation for semilinear nonconservative partial differential equations," Monte Carlo Methods and Applications, De Gruyter, vol. 24(1), pages 55-70, March.
  40. Jana Bielagk & Arnaud Lionnet & Goncalo Dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Papers 1511.04218, arXiv.org, revised Feb 2017.
  41. Akihiko Takahashi & Toshihiro Yamada, 2012. "An Asymptotic Expansion for Forward-Backward SDEs: A Malliavin Calculus Approach," CARF F-Series CARF-F-296, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2013.
  42. Cody B. Hyndman & Polynice Oyono Ngou, 2017. "A Convolution Method for Numerical Solution of Backward Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 1-29, March.
  43. Ren'e Aid & Luciano Campi & Nicolas Langren'e & Huy^en Pham, 2012. "A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation," Papers 1210.8175, arXiv.org.
  44. Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2023. "How many inner simulations to compute conditional expectations with least-square Monte Carlo?," Post-Print hal-03770051, HAL.
  45. Ludkovski, Michael & Young, Virginia R., 2008. "Indifference pricing of pure endowments and life annuities under stochastic hazard and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 14-30, February.
  46. Erhan Bayraktar & Arash Fahim, 2011. "A Stochastic Approximation for Fully Nonlinear Free Boundary Parabolic Problems," Papers 1109.5752, arXiv.org, revised Nov 2013.
  47. Thibaut Mastrolia, 2016. "Density analysis of non-Markovian BSDEs and applications to biology and finance," Papers 1602.06101, arXiv.org.
  48. repec:dau:papers:123456789/7101 is not listed on IDEAS
  49. Masaaki Fujii & Akihiko Takahashi, 2015. "Asymptotic Expansion for Forward-Backward SDEs with Jumps," Papers 1510.03220, arXiv.org, revised Sep 2018.
  50. Lucio Fiorin & Gilles Pagès & Abass Sagna, 2019. "Product Markovian Quantization of a Diffusion Process with Applications to Finance," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1087-1118, December.
  51. Maximilien Germain & Joseph Mikael & Xavier Warin, 2022. "Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2557-2586, December.
  52. Ivan Guo & Nicolas Langren'e & Jiahao Wu, 2023. "Simultaneous upper and lower bounds of American option prices with hedging via neural networks," Papers 2302.12439, arXiv.org, revised Apr 2024.
  53. repec:dau:papers:123456789/5522 is not listed on IDEAS
  54. Mustafa Akan & Barış Ata, 2009. "Bid-Price Controls for Network Revenue Management: Martingale Characterization of Optimal Bid Prices," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 912-936, November.
  55. Masaaki Fujii, 2014. "A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing," CARF F-Series CARF-F-343, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Dec 2014.
  56. Céline Labart & Jérôme Lelong, 2011. "A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options," Working Papers hal-00567729, HAL.
  57. Masaaki Fujii & Akihiko Takahashi, 2018. "Asymptotic Expansion for Forward-Backward SDEs with JumpsAsymptotic Expansion for Forward-Backward SDEs with Jumps (Forthcoming in Stochastics) (Revised version of F-372)," CARF F-Series CARF-F-445, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  58. Aïd, René & Campi, Luciano & Langrené, Nicolas & Pham, Huyên, 2014. "A probabilistic numerical method for optimal multiple switching problems in high dimension," LSE Research Online Documents on Economics 63011, London School of Economics and Political Science, LSE Library.
  59. Lorenc Kapllani & Long Teng, 2024. "A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations," Papers 2404.08456, arXiv.org.
  60. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.
  61. Masaaki Fujii & Akihiko Takahashi, 2016. "Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-term Expansions," Papers 1606.04285, arXiv.org, revised May 2018.
  62. Masaaki Fujii, 2014. "A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing," CIRJE F-Series CIRJE-F-931, CIRJE, Faculty of Economics, University of Tokyo.
  63. Samuel N. Cohen & Lukasz Szpruch, 2011. "On Markovian solutions to Markov Chain BSDEs," Papers 1111.5739, arXiv.org.
  64. Dirk Becherer & Plamen Turkedjiev, 2014. "Multilevel approximation of backward stochastic differential equations," Papers 1412.3140, arXiv.org.
  65. Christian Bender & Nikolaus Schweizer, 2019. "`Regression Anytime' with Brute-Force SVD Truncation," Papers 1908.08264, arXiv.org, revised Oct 2020.
  66. Mastrolia, Thibaut, 2018. "Density analysis of non-Markovian BSDEs and applications to biology and finance," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 897-938.
  67. Masaaki Fujii & Akihiko Takahashi, 2016. "Solving Backward Stochastic Differential Equations by Connecting the Short-term Expansions," CIRJE F-Series CIRJE-F-1016, CIRJE, Faculty of Economics, University of Tokyo.
  68. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2019. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs (Forthcoming in Asia-Pacific Financial Markets)," CARF F-Series CARF-F-456, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  69. Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2023. "How Many Inner Simulations to Compute Conditional Expectations with Least-square Monte Carlo?," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-25, September.
  70. Ulrich Horst & Matthias Müller, 2007. "On the Spanning Property of Risk Bonds Priced by Equilibrium," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 784-807, November.
  71. René Aïd & Luciano Campi & Nicolas Langrené & Huyên Pham, 2012. "A probabilistic numerical method for optimal multiple switching problems in high dimension," Working Papers hal-00747229, HAL.
  72. Moez Mrad & Nizar Touzi & Amina Zeghal, 2006. "Monte Carlo Estimation of a Joint Density Using Malliavin Calculus, and Application to American Options," Computational Economics, Springer;Society for Computational Economics, vol. 27(4), pages 497-531, June.
  73. Gong, Benxue & Rui, Hongxing, 2015. "One order numerical scheme for forward–backward stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 220-231.
  74. dos Reis, Gonçalo & Réveillac, Anthony & Zhang, Jianing, 2011. "FBSDEs with time delayed generators: Lp-solutions, differentiability, representation formulas and path regularity," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2114-2150, September.
  75. Chol-Kyu Pak & Mun-Chol Kim & Chang-Ho Rim, 2018. "Adapted $\theta$-Scheme and Its Error Estimates for Backward Stochastic Differential Equations," Papers 1808.02173, arXiv.org.
  76. Andrew Lesniewski & Anja Richter, 2016. "Managing counterparty credit risk via BSDEs," Papers 1608.03237, arXiv.org, revised Aug 2016.
  77. Masaaki Fujii, 2014. "A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing," Papers 1405.0378, arXiv.org, revised Dec 2014.
  78. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2021. "Stability of backward stochastic differential equations: the general case," Papers 2107.11048, arXiv.org, revised Apr 2023.
  79. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CARF F-Series CARF-F-423, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  80. Bendera, Christian & Moseler, Thilo, 2008. "Importance sampling for backward SDEs," CoFE Discussion Papers 08/11, University of Konstanz, Center of Finance and Econometrics (CoFE).
  81. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," Papers 1710.07030, arXiv.org, revised Mar 2019.
  82. Yingming Ge & Lingfei Li & Gongqiu Zhang, 2022. "A Fourier Transform Method for Solving Backward Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 385-412, March.
  83. Ioannis Exarchos & Evangelos Theodorou & Panagiotis Tsiotras, 2019. "Stochastic Differential Games: A Sampling Approach via FBSDEs," Dynamic Games and Applications, Springer, vol. 9(2), pages 486-505, June.
  84. Kraft, Holger & Seifried, Frank Thomas, 2013. "Stochastic differential utility as the continuous-time limit of recursive utility," SAFE Working Paper Series 17, Leibniz Institute for Financial Research SAFE.
  85. Cohen, Samuel N. & Ji, Shaolin & Yang, Shuzhen, 2014. "A generalized Girsanov transformation of finite state stochastic processes in discrete time," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 33-39.
  86. Pelsser Antoon & Gnameho Kossi, 2019. "A Monte Carlo method for backward stochastic differential equations with Hermite martingales," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 37-60, March.
  87. Pagès, Gilles & Sagna, Abass, 2018. "Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 847-883.
  88. Imkeller, Peter & Dos Reis, Gonçalo, 2010. "Path regularity and explicit convergence rate for BSDE with truncated quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 348-379, March.
  89. Qiang Han & Shaolin Ji, 2022. "A Multi-Step Algorithm for BSDEs Based On a Predictor-Corrector Scheme and Least-Squares Monte Carlo," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2403-2426, December.
  90. Li, Danping & Shen, Yang & Zeng, Yan, 2018. "Dynamic derivative-based investment strategy for mean–variance asset–liability management with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 72-86.
  91. Stefan Geiss & Emmanuel Gobet, 2010. "Fractional smoothness and applications in finance," Papers 1004.3577, arXiv.org.
  92. Sébastien Chaumont & Peter Imkeller & Matthias Müller & Ulrich Horst, 2005. "A Simple Model for Trading Climate Risk," Vierteljahrshefte zur Wirtschaftsforschung / Quarterly Journal of Economic Research, DIW Berlin, German Institute for Economic Research, vol. 74(2), pages 175-195.
  93. Masaaki Fujii & Akihiko Takahashi, 2016. "Solving Backward Stochastic Differential Equations by Connecting the Short-term Expansions," CARF F-Series CARF-F-387, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  94. Chol-Kyu Pak & Mun-Chol Kim & O Hun, 2018. "A generalized scheme for BSDEs based on derivative approximation and its error estimates," Papers 1808.02478, arXiv.org.
  95. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2019. "Variance Reduction Applied to Machine Learning for Pricing Bermudan/American Options in High Dimension," Papers 1903.11275, arXiv.org, revised Dec 2019.
  96. Wei Zhang & Hui Min, 2021. "Weak Convergence Analysis and Improved Error Estimates for Decoupled Forward-Backward Stochastic Differential Equations," Mathematics, MDPI, vol. 9(8), pages 1-15, April.
  97. Geiss, Stefan & Ylinen, Juha, 2020. "Weighted bounded mean oscillation applied to backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3711-3752.
  98. Bally Vlad & Caramellino Lucia & Zanette Antonino, 2005. "Pricing and hedging American options by Monte Carlo methods using a Malliavin calculus approach," Monte Carlo Methods and Applications, De Gruyter, vol. 11(2), pages 97-133, June.
  99. Bouchard, Bruno & Elie, Romuald, 2008. "Discrete-time approximation of decoupled Forward-Backward SDE with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 53-75, January.
  100. Pierre del Moral & Peng Hu & Nadia Oudjane & Bruno Rémillard, 2010. "On the Robustness of the Snell envelope," Working Papers inria-00487103, HAL.
  101. Stefan Geiss & Emmanuel Gobet, 2011. "Fractional smoothness and applications in Finance," Post-Print hal-00474803, HAL.
  102. Deng Ding & Xiaofei Li & Yiqi Liu, 2017. "A regression-based numerical scheme for backward stochastic differential equations," Computational Statistics, Springer, vol. 32(4), pages 1357-1373, December.
  103. Callegaro, Giorgia & Gnoatto, Alessandro & Grasselli, Martino, 2023. "A fully quantization-based scheme for FBSDEs," Applied Mathematics and Computation, Elsevier, vol. 441(C).
  104. Matoussi Anis & Sabbagh Wissal, 2016. "Numerical computation for backward doubly SDEs with random terminal time," Monte Carlo Methods and Applications, De Gruyter, vol. 22(3), pages 229-258, September.
  105. Masaaki Fujii, 2016. "A polynomial scheme of asymptotic expansion for backward SDEs and option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 427-445, March.
  106. W. Ackooij & X. Warin, 2020. "On conditional cuts for stochastic dual dynamic programming," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 173-199, June.
  107. Labart Céline & Lelong Jérôme, 2013. "A parallel algorithm for solving BSDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 19(1), pages 11-39, March.
  108. Weinan E & Martin Hutzenthaler & Arnulf Jentzen & Thomas Kruse, 2021. "Multilevel Picard iterations for solving smooth semilinear parabolic heat equations," Partial Differential Equations and Applications, Springer, vol. 2(6), pages 1-31, December.
  109. Jana Bielagk & Arnaud Lionnet & Gonçalo dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Working Papers hal-01245812, HAL.
  110. Akihiko Takahashi & Toshihiro Yamada, 2012. "An Asymptotic Expansion for Forward-Backward SDEs; A Malliavin Calculus Aproach," CIRJE F-Series CIRJE-F-865, CIRJE, Faculty of Economics, University of Tokyo.
  111. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2019. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDEs," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(3), pages 391-408, September.
  112. Steven Kou & Xianhua Peng & Xingbo Xu, 2016. "EM Algorithm and Stochastic Control in Economics," Papers 1611.01767, arXiv.org.
  113. Masaaki Fujii & Akihiko Takahashi, 2016. "Solving Backward Stochastic Differential Equations by Connecting the Short-term Expansions(Revised version of CARF-F-387)," CARF F-Series CARF-F-398, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  114. Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2022. "How many inner simulations to compute conditional expectations with least-square Monte Carlo?," Working Papers hal-03770051, HAL.
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