Graduate School of Economics
YAMADA Toshihiro

Papers

1. Weak approximation of SDEs for tempered distributions and applications (Peer-reviewed)
Yuga Iguchi, Toshihiro Yamada
Advances in Computational Mathematics (to appear) 2022.5
2. A weak approximation method for irregular functionals of hypoelliptic diffusions (Peer-reviewed)
Naho Akiyama, Toshihiro Yamada
Applied Numerical Mathematics 2022.2
3. 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
4. A Gaussian Kusuoka-approximation without solving random ODEs (Peer-reviewed)
Toshihiro Yamada
SIAM Journal on Financial Mathematics 2022.1
5. 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
IEEE CIFEr 2022 2022
6. 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
7. Numerical methods for backward stochastic differential equations: a survey
Jared Chessari, Reiichiro Kawai, Yuji Shinozaki, Toshihiro Yamada
arXiv 2022
8. 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
9. Deep Asymptotic Expansion: application to financial mathematics (Peer-reviewed)
Yuga Iguchi, Riu Naito, Yusuke Okano, Akihiko Takahashi, Toshihiro Yamada
IEEE CSDE 2021 (to appear) 2021.12
10. A higher order weak approximation of McKean-Vlasov type SDEs (Peer-reviewed)
Riu Naito, Toshihiro Yamada
BIT Numerical Mathematics 2021.6
11. High order weak approximation for irregular functionals of time-inhomogeneous SDEs (Peer-reviewed)
Toshihiro Yamada
Monte Carlo Methods and Applications 2021
12. Acceleration of automatic differentiation of solutions to parabolic partial differential equations: a higher order discretization (Peer-reviewed)
Kimiki Tokutome, Toshihiro Yamada
Numerical Algorithms Vol.86,pp.593-635 2021
13. A second order discretization for degenerate systems of stochastic differential equations (Peer-reviewed)
Yuga Iguchi, Toshihiro Yamada
IMA Journal of Numerical Analysis 2021
14. Discrete Bismut formula: Conditional integration by parts and a representation for delta hedging process (Peer-reviewed)
Naho Akiyama, Toshihiro Yamada
Risk and Decision Analysis 2021
15. 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 Vol.55,pp.323-367 2021
16. An acceleration scheme for deep learning-based BSDE solver using weak expansions (Peer-reviewed)
Riu Naito, Toshihiro Yamada
International Journal of Financial Engineering 2020
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. A Malliavin calculus approach with asymptotic expansion in computational finance (Peer-reviewed)
Toshihiro Yamada
Ph.D. Thesis, The University of Tokyo 2015
33. 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
34. 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
35. 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
36. 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
37. 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
38. 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
39. 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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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