Graduate School of Economics
YAMADA Toshihiro

Papers

1. A weak approximation for Bismut’s formula: an algorithmic differentiation method (Peer-reviewed)
Naho Akiyama, Toshihiro Yamada
Mathematics and Computers in Simulation 2024.2
doi
2. Asymptotic expansion and weak approximation for a stochastic control problem on path space (Peer-reviewed)
Masaya Kannari, Riu Naito, Toshihiro Yamada
Entropy 2024.1
doi
3. Pricing high-dimensional Bermudan options using deep learning and high-order weak approximation (Peer-reviewed)
Riu Naito, Toshihiro Yamada
Journal of Computational Finance (to appear) 2024
4. 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
doi
5. 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
doi
6. 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
doi
7. 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
doi
8. Total variation bound for Milstein scheme without iterated integrals (Peer-reviewed)
Toshihiro Yamada
Monte Carlo Methods and Applications 2023.5
doi
9. Numerical methods for backward stochastic differential equations: a survey (Peer-reviewed)
Jared Chessari, Reiichiro Kawai, Yuji Shinozaki, Toshihiro Yamada
Probability Surveys 2023.4
10. 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
doi
11. Weak approximation of SDEs for tempered distributions and applications (Peer-reviewed)
Yuga Iguchi, Toshihiro Yamada
Advances in Computational Mathematics 2022.8
doi
12. 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
doi
13. 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
doi
14. 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
doi
15. A weak approximation method for irregular functionals of hypoelliptic diffusions (Peer-reviewed)
Naho Akiyama, Toshihiro Yamada
Applied Numerical Mathematics 2022.2
doi
16. 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
doi
17. A Gaussian Kusuoka-approximation without solving random ODEs (Peer-reviewed)
Toshihiro Yamada
SIAM Journal on Financial Mathematics 2022.1
doi
18. Deep Asymptotic Expansion: application to financial mathematics (Peer-reviewed)
Yuga Iguchi, Riu Naito, Yusuke Okano, Akihiko Takahashi, Toshihiro Yamada
IEEE CSDE 2021 2021.12
doi
19. A second order discretization for degenerate systems of stochastic differential equations (Peer-reviewed)
Yuga Iguchi, Toshihiro Yamada
IMA Journal of Numerical Analysis 2021.10
doi
20. A higher order weak approximation of McKean-Vlasov type SDEs (Peer-reviewed)
Riu Naito, Toshihiro Yamada
BIT Numerical Mathematics 2021.7
21. High order weak approximation for irregular functionals of time-inhomogeneous SDEs (Peer-reviewed)
Toshihiro Yamada
Monte Carlo Methods and Applications 2021.2
doi
22. 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
doi
23. 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
doi
24. An acceleration scheme for deep learning-based BSDE solver using weak expansions (Peer-reviewed)
Riu Naito, Toshihiro Yamada
International Journal of Financial Engineering 2020
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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
doi
34. 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
doi
35. 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
doi
36. 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
37. 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
doi
38. 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
doi
39. 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
40. A Malliavin calculus approach with asymptotic expansion in computational finance (Peer-reviewed)
Toshihiro Yamada
Ph.D. Thesis, The University of Tokyo 2015
41. 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
42. 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
doi
43. 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
Link
44. 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
doi Link
45. 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
doi
46. 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
47. 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
doi

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Presentations

No. Name of subject/Conference Name Year Site
1. 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)
2. A Risk Analysis for the Space Industry(THE 54th IKKYOSAI (Hitotsubashi University))
Holding date :
Presentation date : 2023.11.25
Hitotsubashi University
3. Some approaches to computing integrals of certain functionals on path space(Workshop, Hitotsubashi University)
Holding date :
Presentation date : 2023.10.27
Hitotsubashi University
4. 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
5. New deep learning-based algorithms for high-dimensional Bermudan option pricing(ICIAM2023 (Waseda University))
Holding date :
Presentation date : 2023.8.24
Waseda University
6. Extended Milstein scheme for hypoelliptic diffusions(ICIAM2023 (Waseda University))
Holding date :
Presentation date : 2023.8.24
Waseda University
7. 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
8. Deep learning and probabilistic methods for solving high-dimensional nonlinear PDEs and applications(SCI’23 (Kyoto))
Holding date :
Presentation date : 2023.5
Kyoto
9. 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
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
17. Deep Asymptotic Expansion: Application to Financial Mathematics(IEEE CSDE 2021 (Queensland, Brisbane, Australia))
Holding date :
Presentation date : 2021.12.8
Australia
18. 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
19. 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
20. 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
21. 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
22. 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
23. Numerical scheme for SDEs: A discretization of density(Math Finance Seminar)
Holding date :
Presentation date : 2019.11.22
Tokyo
24. 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
25. Second order discretization of Bismut-Elworthy-Li formula and applications(Stochastic Processes and Related Topics)
Holding date :
Presentation date : 2019.2.21
Kansai University
26. Second order discretization of Bismut-Elworthy-Li formula: application to sensitivity analysis(Workshop, Hitotsubashi University)
Holding date :
Presentation date : 2018.12.14
Hitotsubashi University
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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
34. 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
35. A weak approximation of SDEs and its related topics(Ritsumeikan Math-Fin Seminar)
Holding date :
Presentation date : 2015.9.4
Ritsumeikan University
36. Discretization of vol-of-vol expansion(Operations Research Society of Japan)
Holding date :
Presentation date : 2015.8.5
Wakkanai, Hokkaido
37. A new second order weak approximation of SDEs with application to finance(Workshop, Hitotsubashi University)
Holding date :
Presentation date : 2015.7.10
Hitotsubashi University
38. 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
39. Weak approximation with asymptotic expansion: Application to computational finance(Yokohama National University)
Holding date :
Presentation date : 2015.6.4
Yokohama National University
40. Asymptotics for computational finance(NUS-U Tokyo Workshop on Quantitative Finance)
Holding date :
Presentation date : 2014.9.26
The University of Tokyo
41. 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
42. 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
43. 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
44. Asymptotic Expansion for Forward-Backward SDEs(NUS-U Tokyo Workshop on Quantitative Finance)
Holding date :
Presentation date : 2013.9.27
National University of Singapore
45. 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
46. 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
47. 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
48. 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
49. 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
50. 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
51. 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
52. 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

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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