Research Fields   

Financial Mathematics,  Stochastic Numerical Analysis

Ph.D.  

 University of Tokyo  (2015)

Career 

• April 2023 - present,  Full Professor,  Graduate School of Economics,  Hitotsubashi University

• January-March 2022,  Guest Associate Professor,  Graduate School of Engineering Science,  Osaka University

• March 2018 - March 2023,  Associate Professor,  Graduate School of Economics,  Hitotsubashi University  

• March 2015 - February 2018,  Assistant Professor,  Graduate School of Economics,  Hitotsubashi University

• April 2009 - February 2015,  Researcher,  Mitsubishi UFJ Trust Investment Technology (MTEC)

Academic and Social Affiliations

• Director  of  Center for Financial Engineering Education,  Hitotsubashi University

• Director  of  Japanese Association of Financial Econometrics and Engineering

• PRESTO Researcher  (さきがけ研究員),  Japan Science and Technology Agency (JST)  (November 2020 - March 2024)

• Fellow  of  Kyoto Lab  (京都ラボ / 上席研究員)

• Associate Editor  of  Asia Pacific Financial Markets

Teaching 

• 2022,  Department of Mathematics,  Kyoto University

• 2021,  Graduate School of Engineering Science,  Osaka University

• 2016 - 2017, 2021,  Graduate School of Management,  Tokyo Metropolitan University

• 2015 - 2024,  Graduate School of Informatics and Engineering,   University of Electro-Communications

• 2015,  Department of Mathematical Sciences,  Ritsumeikan University 

• 2015 - present,  Graduate School of Economics,  Hitotsubashi University

Papers

1. New asymptotic expansion formula via Malliavin calculus and its application to rough differential equation driven by fractional Brownian motion (with Akihiko Takahashi), Asymptotic Analysis (to appear) (2024)

2. Pricing high-dimensional Bermudan options using deep learning and high-order weak approximation (with Riu Naito), Journal of Computational Finance (to appear) (2024)

3. Deep learning-based expansion around elliptic diffusions (with Riu Naito), IEEE CSDE 2023  (to appear) (2024)

4. Asymptotic expansion and weak approximation for a stochastic control problem on path space (with Masaya Kannari and Riu Naito), Entropy  (to appear)  (2024)

5. A weak approximation for Bismut's formula: an algorithmic differentiation method (with Naho Akiyama), Mathematics and Computers in Simulation (to appear) (2024)

6. Deep Kusuoka approximation: high-order spatial approximation for solving high-dimensional Kolmogorov equations and its application to finance (with Riu Naito), Computational Economics  (to appear) (2023)

7. Deep high order splitting method for semilinear degenerate PDEs and application to high dimensional nonlinear pricing models (with Riu Naito), Digital Finance  (to appear) (2023) 

8. Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus (with Akihiko Takahashi), Partial Differential Equations and Applications (to appear) (2023)

9. Total variation bound for Milstein scheme without iterated integrals, Monte Carlo Methods and Applications  (to appear) (2023)

10. Numerical methods for backward stochastic differential equations: A survey (with Jared Chessari, Reiichiro Kawai, Yuji Shinozaki), Probability Surveys  (to appear) (2023)

11. A new algorithm for computing path integrals and weak approximation of SDEs inspired by large deviations and Malliavin calculus, Applied Numerical Mathematics  (to appear) (2023) 

12. Weak approximation of SDEs for tempered distributions and applications (with Yuga Iguchi), Advances in Computational Mathematics , vol 48 (5), 52 (2022)

13. A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver (with Akihiko Takahashi and Yoshifumi Tsuchida), Journal of Computational Physics, vol 454, 110956 (2022)

14. Deep weak approximation of SDEs: a spatial approximation scheme for solving Kolmogorov equations (with Riu Naito), International Journal of Computational Methods, vol 19 (8) (2022)

15. A high order weak approximation for jump-diffusions using Malliavin calculus and operator splitting (with Naho Akiyama), Monte Carlo Methods and Applications, vol 28 (2), 97-110  (2022)

16. A deep learning-based high-order operator splitting method for high-dimensional  nonlinear parabolic PDEs via Malliavin calculus: application to CVA computation (with Riu Naito), IEEE CIFEr 2022  (2022) 

17. A Gaussian Kusuoka-approximation without solving random ODEs, SIAM Journal on Financial Mathematics, vol 13 (1), SC1-11 (2022)

18. A weak approximation method for irregular functionals of hypoelliptic diffusions (with Naho Akiyama), Applied Numerical Mathematics, vol 172, 27-49 (2022)

19. A higher order weak approximation of McKean-Vlasov type SDEs (with Riu Naito), BIT Numerical Mathematics, vol 62, 521-559 (2022)

20. Deep Asymptotic Expansion: Application to financial mathematics (with Yuga Iguchi, Riu Naito, Yusuke Okano and Akihiko Takahashi), IEEE CSDE 2021  (2021)

21. Discrete Bismut formula: Conditional integration by parts and a representation for delta hedging process (with Naho Akiyama), Risk and Decision Analysis (2021)

22. High order weak approximation for irregular functionals of time-inhomogeneous SDEs, Monte Carlo Methods and Applications, vol 27 (2), 117-136 (2021)

23. Operator splitting around Euler-Maruyama scheme and high order discretization of heat kernels (with Yuga Iguchi), ESAIM: Mathematical Modelling and Numerical Analysis, vol 55, 323-367 (2021)

24. Acceleration of automatic differentiation of solutions to parabolic partial differential equations: a higher order discretization (with Kimiki Tokutome), Numerical Algorithms, vol 85, 593-635  (2021)

25. A second order discretization for degenerate systems of stochastic differential equations (with Yuga Iguchi), IMA Journal of Numerical Analysis, vol 41 (4), 2782-2829  (2021)

26. An acceleration scheme for deep learning-based BSDE solver using weak expansions (with Riu Naito), International Journal of Financial Engineering, vol 7 (2), 2050012 (2020)

27. A second-order discretization with Malliavin weight and Quasi Monte Carlo method for option pricing (with Kenta Yamamoto), Quantitative Finance, vol 20 (11), 1825-1837 (2020)

28. A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus (with Riu Naito), Monte Carlo Methods and Applications, vol 25 (4) (2019)

29. A control variate method for weak approximation of SDEs via discretization of numerical error of asymptotic expansion (with Yusuke Okano), Monte Carlo Methods and Applications, vol 25 (3) (2019)

30. A third-order weak approximation of multidimensional Ito stochastic differential equations (with Riu Naito), Monte Carlo Methods and Applications, vol 25 (2), 97-120 (2019)

31. An arbitrary high order weak approximation of SDE and Malliavin Monte Carlo: analysis of probability distribution functions, SIAM Journal on Numerical Analysis, vol 57 (2), 563-591 (2019)

32. Second order discretization of Bismut-Elworthy-Li formula: application to sensitivity analysis (with Kenta Yamamoto), SIAM/ASA Journal on Uncertainty Quantification, vol 7 (1), 143-173 (2019)

33. A second-order weak approximation of SDEs using Markov chain without Levy area simulation (with Kenta Yamamoto), Monte Carlo Methods and Applications, 24 (4), 289-308 (2018)

34. Weak Milstein scheme without commutativity condition and its error bound, Applied Numerical Mathematics, vol 131, Sep 2018, 95-108 (2018)

35. A higher order weak approximation scheme of multidimensional stochastic differential equations using Malliavin weights, Journal of Computational and Applied Mathematics, vol 321, Sep 2017, 427-447 (2017)

36. A weak approximation with Malliavin weights for local stochastic volatility model, International Journal of Financial Engineering,  vol 4 (1) (2017)

37. An asymptotic expansion for forward–backward SDEs: a Malliavin calculus approach (with Akihiko Takahashi), Asia-Pacific Financial Markets, 23 (4),  337-373  (2016)

38. A weak approximation with asymptotic expansion and multidimensional Malliavin weights (with Akihiko Takahashi), Annals of Applied Probability, vol 26 (2), 818-856 (2016)

39. On error estimates for asymptotic expansions with Malliavin weights: Application to stochastic volatility model (with Akihiko Takahashi), Mathematics of Operations Research, vol 40 (3), 513-451 (2015)

40. A small noise asymptotic expansion for Young SDE driven by fractional Brownian motion: A sharp error estimate with Malliavin calculus, Stochastic Analysis and Applications, vol 33 (5), 882-902 (2015)

41. An asymptotic expansion of forward-backward SDEs with a perturbed driver (with Akihiko Takahashi), International Journal of Financial Engineering, vol 2 (2) (2015)

42. A formula of small time expansion for Young SDE driven by fractional Brownian motion, Statistics and Probability Letters, vol 101, 64-72 (2015)

43. A Malliavin calculus approach with asymptotic expansion in computational finance, Ph.D Thesis, University of Tokyo (2015)

44. A semigroup expansion for pricing barrier options (with Takashi Kato and Akihiko Takahashi), International Journal of Stochastic Analysis, 2014, 1-15 (2014)

45. Strong convergence for Euler-Maruyama and Milstein schemes with asymptotic method (with Hideyuki Tanaka), International Journal of Theoretical and Applied Finance, vol 17 (2) (2014)

46. An asymptotic expansion formula for up-and-out barrier option price under stochastic volatility model (with Takashi Kato and Akihiko Takahashi), JSIAM Letters, 5, 17-20, (2013)

47. Pricing discrete barrier options under stochastic volatility (with Kenichiro Shiraya and Akihiko Takahashi), Asia-Pacific Financial Markets, vol 19 (3), 205-232 (2012)

48. A remark on approximation of the solutions to partial differential equations in finance (with Akihiko Takahashi), Recent Advances in Financial Engineering 2011,  133-181 (2012)

49. An asymptotic expansion with push-down of Malliavin weights (with Akihiko Takahashi), SIAM Journal on Financial Mathematics, vol 3 (1), 95-136 (2012)

Events

• ICIAM 2023 Tokyo, Recent Development in Stochastic Numerics and Computational Finance  (Organizers: Jiro Akahori, Shoiti Ninomiya and Toshihiro Yamada), Tokyo, 2023

• Stochastics around Finance  (Organizers: Jiro Akahori, Masaaki Fukasawa, Yuri Imamura, Jun Sekine and Toshihiro Yamada), Kanazawa, 2023