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- YAMADA Toshihiro
- Graduate School of Economics
- YAMADA Toshihiro
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Papers
| 1. | Expansion of Bermudan option price using deep learning (Peer-reviewed) Riu Naito, Toshihiro Yamada Recent Development in Stochastic Numerics and Computational Finance (to appear) 2025 |
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| 2. | An extended Milstein scheme for effective weak approximation of diffusions (Peer-reviewed) Yuga Iguchi, Toshihiro Yamada Recent Development in Stochastic Numerics and Computational Finance (to appear) 2025 |
| 3. | Pricing high-dimensional Bermudan options using deep learning and high-order weak approximation (Peer-reviewed) Riu Naito, Toshihiro Yamada Journal of Computational Finance Vol.28,No.1,pp.65-94 2024.6 |
| 4. | New asymptotic expansion formula via Malliavin calculus and its application to rough differential equation driven by fractional Brownian motion (Peer-reviewed) Akihiko Takahashi, Toshihiro Yamada Asymptotic Analysis Vol.140,No.1-2,pp.37-58 2024.5 |
| 5. | A weak approximation for Bismut’s formula: an algorithmic differentiation method (Peer-reviewed) Naho Akiyama, Toshihiro Yamada Mathematics and Computers in Simulation Vol.216,No.February 2024,pp.386-396 2024.2 
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| 6. | Asymptotic expansion and weak approximation for a stochastic control problem on path space (Peer-reviewed) Masaya Kannari, Riu Naito, Toshihiro Yamada Entropy 2024.1
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| 7. | Deep learning-based expansion around elliptic diffusions (Peer-reviewed) Riu Naito, Toshihiro Yamada IEEE CSDE 2023 2024
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| 8. | Discrete Bismut formula: Conditional integration by parts and a representation for delta hedging process (Peer-reviewed) Naho Akiyama, Toshihiro Yamada Risk and Decision Analysis 2023.10
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| 9. | Deep Kusuoka approximation: high-order spatial approximation for solving high-dimensional Kolmogorov equations and its application to finance (Peer-reviewed) Riu Naito, Toshihiro Yamada Computational Economics 2023.10
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| 10. | Deep high order splitting method for semilinear degenerate PDEs and application to high dimensional nonlinear pricing models (Peer-reviewed) Riu Naito, Toshihiro Yamada Digital Finance 2023.8
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| 11. | Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus (Peer-reviewed) Akihiko Takahashi, Toshihiro Yamada Partial Differential Equations and Applications 2023.6
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| 12. | Total variation bound for Milstein scheme without iterated integrals (Peer-reviewed) Toshihiro Yamada Monte Carlo Methods and Applications 2023.5
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| 13. | Numerical methods for backward stochastic differential equations: a survey (Peer-reviewed) Jared Chessari, Reiichiro Kawai, Yuji Shinozaki, Toshihiro Yamada Probability Surveys 2023.4 |
| 14. | A new algorithm for computing path integrals and weak approximation of SDEs inspired by large deviations and Malliavin calculus (Peer-reviewed) Toshihiro Yamada Applied Numerical Mathematics 2023.2
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| 15. | Weak approximation of SDEs for tempered distributions and applications (Peer-reviewed) Yuga Iguchi, Toshihiro Yamada Advances in Computational Mathematics 2022.8
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| 16. | Deep weak approximation of SDEs: a spatial approximation scheme for solving Kolmogorov equations (Peer-reviewed) Riu Naito, Toshihiro Yamada International Journal of Computational Methods 2022.5
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| 17. | A deep learning-based high-order operator splitting method for high-dimensional nonlinear parabolic PDEs via Malliavin calculus: application to CVA computation (Peer-reviewed) Riu Naito, Toshihiro Yamada 2022 IEEE Symposium on Computational Intelligence for Financial Engineering and Economics (CIFEr) 2022.5
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| 18. | A high order weak approximation for jump-diffusions using Malliavin calculus and operator splitting (Peer-reviewed) Naho Akiyama, Toshihiro Yamada Monte Carlo Methods and Applications 2022.2
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| 19. | A weak approximation method for irregular functionals of hypoelliptic diffusions (Peer-reviewed) Naho Akiyama, Toshihiro Yamada Applied Numerical Mathematics 2022.2
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| 20. | A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver (Peer-reviewed) Akihiko Takahashi, Yoshifumi Tsuchida, Toshihiro Yamada Journal of Computational Physics 2022.1
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| 21. | A Gaussian Kusuoka-approximation without solving random ODEs (Peer-reviewed) Toshihiro Yamada SIAM Journal on Financial Mathematics 2022.1
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| 22. | Deep Asymptotic Expansion: application to financial mathematics (Peer-reviewed) Yuga Iguchi, Riu Naito, Yusuke Okano, Akihiko Takahashi, Toshihiro Yamada IEEE CSDE 2021 2021.12
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| 23. | A second order discretization for degenerate systems of stochastic differential equations (Peer-reviewed) Yuga Iguchi, Toshihiro Yamada IMA Journal of Numerical Analysis 2021.10
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| 24. | A higher order weak approximation of McKean-Vlasov type SDEs (Peer-reviewed) Riu Naito, Toshihiro Yamada BIT Numerical Mathematics 2021.7 |
| 25. | High order weak approximation for irregular functionals of time-inhomogeneous SDEs (Peer-reviewed) Toshihiro Yamada Monte Carlo Methods and Applications 2021.2
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| 26. | Acceleration of automatic differentiation of solutions to parabolic partial differential equations: a higher order discretization (Peer-reviewed) Kimiki Tokutome, Toshihiro Yamada Numerical Algorithms 2021.2
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| 27. | Operator splitting around Euler-Maruyama scheme and high order discretization of heat kernels (Peer-reviewed) Yuga Iguchi, Toshihiro Yamada ESAIM: Mathematical Modelling and Numerical Analysis 2021
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| 28. | An acceleration scheme for deep learning-based BSDE solver using weak expansions (Peer-reviewed) Riu Naito, Toshihiro Yamada International Journal of Financial Engineering 2020 |
| 29. | A second order discretization with Malliavin weight and Quasi Monte Carlo method for option pricing (Peer-reviewed) Toshihiro Yamada, Kenta Yamamoto Quantitative Finance Vol.20,No.11 2020 |
| 30. | Second order discretization of Bismut-Elworthy-Li formula: application to sensitivity analysis (Peer-reviewed) Toshihiro Yamada, Kenta Yamamoto SIAM/ASA Journal on Uncertainty Quantification Vol.7,No.01,pp.143-173 2019 |
| 31. | A control variate method for weak approximation of SDEs via discretization of numerical error of asymptotic expansion (Peer-reviewed) Yusuke Okano, Toshihiro Yamada Monte Carlo Methods and Applications Vol.25,No.3 2019 |
| 32. | A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus (Peer-reviewed) Riu Naito, Toshihiro Yamada Monte Carlo Methods and Applications Vol.25,No.4 2019 |
| 33. | An arbitrary high order weak approximation of SDE and Malliavin Monte Carlo: analysis of probability distribution functions (Peer-reviewed) Toshihiro Yamada SIAM Journal on Numerical Analysis Vol.57,No.2,pp.563-591 2019 |
| 34. | A third-order weak approximation of multidimensional Ito stochastic differential equations (Peer-reviewed) Riu Naito, Toshihiro Yamada Monte Carlo Methods and Applications Vol.25,No.2,pp.97-120 2019 |
| 35. | Weak Milstein scheme without commutativity condition and its error bound (Peer-reviewed) Toshihiro Yamada Applied Numerical Mathematics Vol.131,No.2018 (September),pp.95-108 2018.9 |
| 36. | A second order weak approximation of SDEs using Markov chain without Levy area simulation (Peer-reviewed) Toshihiro Yamada, Kenta Yamamoto Monte Carlo Methods and Applications Vol.24,No.04,pp.289-308 2018 |
| 37. | A weak approximation with Malliavin weights for local stochastic volatility model (Peer-reviewed) Toshihiro Yamada International Journal of Financial Engineering Vol.04,No.01 2017
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| 38. | A higher order weak approximation scheme of multidimensional stochastic differential equations using Malliavin weights (Peer-reviewed) Toshihiro Yamada Journal of Computational and Applied Mathematics Vol.321,No.September 2017,pp.427-447 2017
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| 39. | A weak approximation with asymptotic expansion and multidimensional Malliavin weights (Peer-reviewed) Akihiko Takahashi, Toshihiro Yamada Annals of Applied Probability Vol.26,No.2,pp.818-856 2016
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| 40. | An asymptotic expansion for forward–backward SDEs: a Malliavin calculus approach (Peer-reviewed) Akihiko Takahashi, Toshihiro Yamada Asia-Pacific Financial Markets Vol.23,No.4,pp.337-373 2016 |
| 41. | A formula of small time expansion for Young SDE driven by fractional Brownian motion (Peer-reviewed) Toshihiro Yamada Statistics and Probability Letters Vol.101,pp.64-72 2015
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| 42. | On error estimates for asymptotic expansions with Malliavin weights: Application to stochastic volatility model (Peer-reviewed) Akihiko Takahashi, Toshihiro Yamada Mathematics of Operations Research Vol.40,No.3,pp.513-451 2015
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| 43. | A small noise asymptotic expansion for Young SDE driven by fractional Brownian motion: A sharp error estimate with Malliavin calculus (Peer-reviewed) Toshihiro Yamada Stochastic Analysis and Applications Vol.33,No.5,pp.882-902 2015 |
| 44. | A Malliavin calculus approach with asymptotic expansion in computational finance (Peer-reviewed) Toshihiro Yamada Ph.D. Thesis, The University of Tokyo 2015 |
| 45. | An asymptotic expansion of forward-backward SDEs with a perturbed driver (Peer-reviewed) Akihiko Takahashi, Toshihiro Yamada International Journal of Financial Engineering Vol.2,No.2 2015 |
| 46. | A semigroup expansion for pricing barrier options (Peer-reviewed) Takashi Kato, Akihiko Takahashi, Toshihiro Yamada International Journal of Stochastic Analysis Vol.2014,pp.1-15 2014
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| 47. | Strong convergence for Euler-Maruyama and Milstein schemes with asymptotic method (Peer-reviewed) Hideyuki Tanaka, Toshihiro Yamada International Journal of Theoretical and Applied Finance Vol.17,No.2,pp.1450014-1-1450014-22 2014 
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| 48. | An asymptotic expansion formula for up-and-out barrier option price under stochastic volatility model (Peer-reviewed) Takashi Kato, Akihiko Takahashi, Toshihiro Yamada JSIAM Letters Vol.5,pp.17-20 2013
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| 49. | Pricing discrete barrier options under stochastic volatility (Peer-reviewed) Kenichiro Shiraya, Akihiko Takahashi, Toshihiro Yamada Asia-Pacific Financial Markets Vol.19,No.3,pp.205-232 2012.9
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| 50. | A remark on approximation of the solutions to partial differential equations in finance (Peer-reviewed) Akihiko Takahashi, Toshihiro Yamada Recent Advances in Financial Engineering 2011 2012.6 |
| 51. | An asymptotic expansion with push-down of Malliavin weights (Peer-reviewed) Akihiko Takahashi, Toshihiro Yamada SIAM Journal on Financial Mathematics Vol.3,No.1,pp.95-136 2012.1
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Misc.
| 1. | AI時代の数理研究 (数学meets情報科学ーーDX時代の数理研究)
2025 |
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| 2. | Stochastic numerical analysis and deep learning (in Japanese)
Toshihiro Yamada SUGAKU seminar 2024 |
Presentations
| No. | Name of subject/Conference Name | Year | Site |
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| 1. | Numerical methods for stochastic differential equations related to rough path theory(New Trends in Rough Path Analysis) |
Holding date :
Presentation date : 2025.2.14 |
Osaka University |
| 2. | Learning and simulating diffusions and rough paths(A*STAR CFAR-JST Presto Joint Workshop) |
Holding date :
Presentation date : 2025.1.13 |
Singapore |
| 3. | A strong approximation via replication of path-functionals and a new simulation method for financial models(Workshop, Hitotsubashi University) |
Holding date :
Presentation date : 2024.11.29 |
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| 4. | Sampling SDEs via neural network(AQFC 2024 (Asian Quantitative Finance Conference)) |
Holding date :
Presentation date : 2024.8.9 |
Taipei, Taiwan |
| 5. | Neural Network SDE Simulator(ICAM 2024 (International Conference on Analysis Mathematics)) |
Holding date :
Presentation date : 2024.5.31 |
Hong Kong |
| 6. | Remark on expansion for utility indifference pricing problems(JSIAM) |
Holding date :
Presentation date : 2024.3.5 |
Nagaoka University of Technology |
| 7. | Neural Network SDE Simulator(JAFEE) |
Holding date :
Presentation date : 2024.2 |
University of Tokyo |
| 8. | On some approaches to weak approximation of SDEs(Séminaire Bachelier Paris (Institut Henri Poincaré)) |
Holding date :
Presentation date : 2023.12.1 |
Institut Henri Poincaré (Paris, France) |
| 9. | A Risk Analysis for the Space Industry(THE 54th IKKYOSAI (Hitotsubashi University)) |
Holding date :
Presentation date : 2023.11.25 |
Hitotsubashi University |
| 10. | Some approaches to computing integrals of certain functionals on path space(Workshop, Hitotsubashi University) |
Holding date :
Presentation date : 2023.10.27 |
Hitotsubashi University |
| 11. | Numerical methods for solving high dimensional PDEs via deep learning(Research on High-performance Scientific Computing in a New Era (RIMS, Kyoto University)) |
Holding date :
2023.10.18
- 2023.10.20 Presentation date : 2023.10.19 |
Kyoto University |
| 12. | New deep learning-based algorithms for high-dimensional Bermudan option pricing(ICIAM2023 (Waseda University)) |
Holding date :
Presentation date : 2023.8.24 |
Waseda University |
| 13. | Extended Milstein scheme for hypoelliptic diffusions(ICIAM2023 (Waseda University)) |
Holding date :
Presentation date : 2023.8.24 |
Waseda University |
| 14. | Deep learning and probabilistic methods for solving high-dimensional partial differential equations and applications(Numerical Analysis Seminar (UTNAS) (University of Tokyo)) |
Holding date :
Presentation date : 2023.6 |
The University of Tokyo |
| 15. | Deep learning and probabilistic methods for solving high-dimensional nonlinear PDEs and applications(SCI’23 (Kyoto)) |
Holding date :
Presentation date : 2023.5 |
Kyoto |
| 16. | Total variation bound for Milstein scheme without iterated integrals(Osaka-UCL Mini-Workshop on Stochastics, Numerics and Risk (Osaka University)) |
Holding date :
Presentation date : 2023.2 |
Osaka University |
| 17. | Deep learning and probabilistic approximation schemes for solving high-dimensional PDEs(Workshop on Stochastic processes and applications (National Institute of Informatics)) |
Holding date :
Presentation date : 2023.1 |
National Institute of Informatics |
| 18. | Asymptotic expansion and deep neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with nonlinear coefficients(Workshop, Hitotsubashi University) |
Holding date :
Presentation date : 2022.11.25 |
Hitotsubashi University |
| 19. | A discretization method of stochastic differential equation and its applications(Colloquium, Department of Mathematics, Kyoto University) |
Holding date :
Presentation date : 2022.11.9 |
Kyoto University |
| 20. | Solving nonlinear pricing problems in high dimension using deep learning and high order discretization schemes(Ajou Workshop on Financial Engineering (Ajou University)) |
Holding date :
Presentation date : 2022.9 |
Ajou University |
| 21. | Total variation bounds for Milstein scheme and Euler-Maruyama scheme: application to mathematical finance(1st Seoul-London Workshop on Mathematical Finance (Seoul National University)) |
Holding date :
Presentation date : 2022.9 |
Seoul National University |
| 22. | A deep learning-based high-order operator splitting method for high-dimensional nonlinear parabolic PDEs via Malliavin calculus: application to CVA computation(2022 IEEE Computational Intelligence for Financial Engineering and Economics (Helsinki, Finland)) |
Holding date :
Presentation date : 2022.5 |
Helsinki |
| 23. | Deep learning and probabilistic methods for solving high-dimensional linear/nonlinear parabolic PDEs(One World: Stochastic Numerics and Inverse Problems (United Kingdom)) |
Holding date :
Presentation date : 2021.12.15 |
United Kingdom |
| 24. | Deep Asymptotic Expansion: Application to Financial Mathematics(IEEE CSDE 2021 (Queensland, Brisbane, Australia)) |
Holding date :
Presentation date : 2021.12.8 |
Australia |
| 25. | A Gaussian Kusuoka approximation and application to deep learning-based numerical method for high-dimensional PDEs(4th KAFE-JAFEE International Symposium on Financial Engineering (Tokyo)) |
Holding date :
Presentation date : 2021.8.21 |
Tokyo |
| 26. | Machine learning and probabilistic methods for solving high-dimensional partial differential equations(Osaka University Center for Mathematical Modeling and Data Science (Osaka University)) |
Holding date :
Presentation date : 2021.1.22 |
Osaka University |
| 27. | Operator splitting around Euler-Maruyama scheme and high order discretization of heat kernels: application to finance(Workshop, Hitotsubashi University) |
Holding date :
Presentation date : 2020.10.23 |
Hitotsubashi University |
| 28. | Higher order weak approximation for SDEs and BSDEs of McKean-Vlasov type(Ritsumeikan Math-Fin Seminar) |
Holding date :
Presentation date : 2020.7.23 |
Ritsumeikan University |
| 29. | High order weak approximation for SDEs and automatic differentiation: application to BSDEs(Osaka University Nakanoshima Workshop) |
Holding date :
Presentation date : 2019.11.28 |
Osaka University |
| 30. | Numerical scheme for SDEs: A discretization of density(Math Finance Seminar) |
Holding date :
Presentation date : 2019.11.22 |
Tokyo |
| 31. | An arbitrary high order weak approximation of SDE and Malliavin Monte Carlo: application to BSDE(Workshop, Hitotsubashi University) |
Holding date :
Presentation date : 2019.11.15 |
Hitotsubashi University |
| 32. | Second order discretization of Bismut-Elworthy-Li formula and applications(Stochastic Processes and Related Topics) |
Holding date :
Presentation date : 2019.2.21 |
Kansai University |
| 33. | Second order discretization of Bismut-Elworthy-Li formula: application to sensitivity analysis(Workshop, Hitotsubashi University) |
Holding date :
Presentation date : 2018.12.14 |
Hitotsubashi University |
| 34. | Higher order discretization methods using Malliavin Monte Carlo and Brownian Markov chain without Levy area simulation(WORKSHOP ON "MATHEMATICAL FINANCE AND RELATED ISSUES") |
Holding date :
Presentation date : 2018.3.12 |
Osaka University |
| 35. | Weak Milstein scheme without commutativity condition and its sharp asymptotic error bound(一橋大学経済統計ワークショップ) |
Holding date :
Presentation date : 2017.11.17 |
Hitotsubashi University |
| 36. | A second order discretization method for the Delta(Osaka-UCL Workshop on Stochastics, Numerics and Risk (Osaka University)) |
Holding date :
Presentation date : 2017.3.30 |
Osaka University |
| 37. | A general formula for weak approximation with multidimensional Malliavin weights: application to option pricing(Hitotsubashi University) |
Holding date :
Presentation date : 2016.10.14 |
Hitotsubashi University |
| 38. | On higher order weak approximation with Malliavin weights(Hitotsubashi University ICS FS (Faculty Seminar)) |
Holding date :
Presentation date : 2016.7.4 |
International Corporate Strategy, Hitotsubashi University |
| 39. | A weak approximation of SDEs: application to computational finance(Joint International Research Open (UK)) |
Holding date :
Presentation date : 2016.3.1 |
University of Liverpool, United Kingdom |
| 40. | A weak approximation of SDEs: application to computational finance(Winter Workshop on Operations Research, Finance and Mathematics, 2016) |
Holding date :
Presentation date : 2016.2.17 |
Hokkaido |
| 41. | A weak approximation scheme for SDEs and applications to finance(Stochastic Methods in Finance, Insurance and Statistics (Australia)) |
Holding date :
Presentation date : 2015.12.10 |
Shoal Bay, Australia |
| 42. | A weak approximation of SDEs and its related topics(Ritsumeikan Math-Fin Seminar) |
Holding date :
Presentation date : 2015.9.4 |
Ritsumeikan University |
| 43. | Discretization of vol-of-vol expansion(Operations Research Society of Japan) |
Holding date :
Presentation date : 2015.8.5 |
Wakkanai, Hokkaido |
| 44. | A new second order weak approximation of SDEs with application to finance(Workshop, Hitotsubashi University) |
Holding date :
Presentation date : 2015.7.10 |
Hitotsubashi University |
| 45. | A new second order weak approximation of SDEs(慶應義塾大学計量経済学ワークショップ) |
Holding date :
Presentation date : 2015.6.23 |
Keio University |
| 46. | Weak approximation with asymptotic expansion: Application to computational finance(Yokohama National University) |
Holding date :
Presentation date : 2015.6.4 |
Yokohama National University |
| 47. | Asymptotics for computational finance(NUS-U Tokyo Workshop on Quantitative Finance) |
Holding date :
Presentation date : 2014.9.26 |
The University of Tokyo |
| 48. | Asymptotic Methods for Backward SDEs and Nonlinear Pricing(Mathematical Modeling and Data Science seminar (Center for the Study of Finance and Insurance, Osaka University)) |
Holding date :
Presentation date : 2014.5.30 |
Osaka University |
| 49. | Operator splitting using asymptotic expansion and application to computational finance (in Japanese)(日本応用数理学会研究部会連合発表会) |
Holding date :
Presentation date : 2014.3.19 |
Kyoto University |
| 50. | Asymptotic Methods for Computational Finance(大阪大学中之島ワークショップ (大阪大学)) |
Holding date :
Presentation date : 2013.12.6 |
Osaka University |
| 51. | Asymptotic Expansion for Forward-Backward SDEs(NUS-U Tokyo Workshop on Quantitative Finance) |
Holding date :
Presentation date : 2013.9.27 |
National University of Singapore |
| 52. | Asymptotic expansion for forward-backward SDEs and numerical method for computing CVA (in Japanese)(日本応用数理学会2013年度年会) |
Holding date :
Presentation date : 2013.9.10 |
Fukuoka |
| 53. | Asymptotic Expansion for Forward-Backward SDEs and CVA(39th JAFEE Meeting (Japanese Association of Financial Econometrics and Engineering)) |
Holding date :
Presentation date : 2013.8.4 |
Meiji University |
| 54. | Asymptotic Formulas in Local and Stochastic Volatility Models(JAFEE（日本金融・証券計量・工学学会）デリバティブ部会) |
Holding date :
Presentation date : 2013.3.2 |
Tokyo |
| 55. | A closed-form approximation method for computational finance(立命館大学数理科学研究科解析セミナー) |
Holding date :
Presentation date : 2013.1.18 |
Ritsumeikan University |
| 56. | Numerical approximation for forward-backward SDEs via asymptotic expansion (in Japanese)(数理ファイナンス合宿型セミナー) |
Holding date :
Presentation date : 2012.11.3 |
Tokyo |
| 57. | On expansion formula for barrier option prices (in Japanese)(日本応用数理学会2012年度年会) |
Holding date :
Presentation date : 2012.8.30 |
Hokkaido |
| 58. | Strong approximation of SDEs using asymptotic expansion and multilevel Monte Carlo simulation (in Japanese)(日本応用数理学会2012年度年会) |
Holding date :
Presentation date : 2012.8.30 |
Hokkaido |
| 59. | An Asymptotic Expansion for Solutions of Cauchy-Dirichlet Problem for Second Order Parabolic PDEs and its Application to Pricing Barrier Options(37th JAFEE Meeting (Japanese Association of Financial Econometrics and Engineering)) |
Holding date :
Presentation date : 2012.8.4 |
Seijyo University |
Awards
| No. | Award name | Year |
|---|---|---|
| 1. | JAFEE BEST PAPER AWARD | 2016.1 |
Research Projects
| No. | Research subject | Research item(Awarding organization, System name) | Year |
|---|---|---|---|
| 1. | New computational method for high dimensional PDEs using Malliavin calculus and deep learning
|
Sakigake (PRESTO)
( Awarding organization: Japan Science and Technology Agency (JST) ) |
2020.11 - 2024.3 |
| 2. | A new automatic differentiation and its application to computational finance
|
Grant-in-Aid for Young Scientists
( System name: Grants-in-Aid for Scientific Research ) |
2019.4 - 2021.3 |
| 3. | Quantitative risk measurement in insurance and finance
|
( Awarding organization: Tokio Marine Kagami Memorial Foundation System name: 社会科学研究助成 ) |
2018.1 - 2019.3 |
| 4. | New higher order discretization method with Malliavin calculus
|
Challenging Exploratory Research
( System name: Grants-in-Aid for Scientific Research ) |
2016.4 - 2019.3 |
