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Nakano Lab

Yumiharu Nakano’s Lab

Department of Mathematical and Computing Science, School of Computing, Institute of Science Tokyo​

Research Themes​

Computational mathematics for stochastic control, optimal transport, and inference

Topics​

  • Numerical analysis of HJB equations and stochastic optimal control
  • Kernel-based methods for Schrödinger bridges and optimal transport
  • Filtering and inverse problems for stochastic systems
  • Applications: generative models, mathematical finance and insurance
Members (AY 2026)
NAKANO, YumiharuAssociate Professornakano(at)comp.isct.ac.jp
KANEKO, TatsuyaM2
CHEN, YuzhouM2
HIRATA, RyujiM2
KATSUBE, TaiyoM2
TAKEMOTO, HirokiM2
YAGI, TsubasaM2
CHENG, ZixuanM1
LI, ChiM1
FUKUMORI, RyuseiB4
MITA, AkinoriB4
YASHIRO, KyotaB4
UEDA, LeonardoB3
Papers
  • Y. Nakano. Kernel-based potential mean-field games with unbiased random Fourier U-statistics. arXiv:2605.29371[math.OC] [code]
  • Y. Nakano. Continuum-marginal optimal transport: a mesh-free kernel method. arXiv:2604.24226[math.OC] [code]
  • Y. Nakano. Inverse stochastic control via generalized Schrödinger problems. arXiv:2601.09210[math.OC]
  • Y. Nakano and T. Saito. A deep learning approach to multi-marginal optimal transport via Hilbert space embeddings of probability measures. Statist. Comput., 36 (2026), 118. [code]
  • Y. Nakano. Structural and convergence analysis of discrete-time denoising diffusion probabilistic models. arxiv:2406.01320[math.PR]
  • Y. Nakano. A kernel-based method for Schrödinger bridges. Jpn. J. Ind. Appl. Math., 43 (2026), 46. [code]
  • Y. Nakano. Convergence of differentiable non-monotone schemes for fully nonlinear parabolic equations. arXiv:1803.09446[math.NA].
  • T. Saito and Y. Nakano. Solving Monge Problem by Hilbert Space Embeddings of Probability Measures, Proceedings of the 14th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, SciTePress, pp. 294-300, 2025. (See also arXiv:2412.03478[math.OC].)
  • K. Endo and Y. Nakano. Weak approximation of Schrödinger-Föllmer diffusion, Statist. Probab. Lett., 213 (2024), 110171.
  • Y. Nakano, Inverse stochastic optimal controls, Automatica, 149 (2023), 110831.
  • Y. Kinoshita and Y. Nakano. Kernel-based collocation methods for Heath-Jarrow-Morton models with Musiela parametrization, Stochastics, 93 (2021), 921-944.
  • Y. Nakano. Numerical analysis of Zakai equations by kernel collocation methods, Systems, Control and Information, 64 (2020), 258-263. (in Japanese)
  • Y. Nakano. Kernel collocation methods for nonlinear partial differential equations, Bulletin of the Japan Society for Industrial and Applied Mathematics, 4 (2019), 18-25. (in Japanese)
  • Y. Nakano. Kernel-based collocation methods for Zakai equations, Stoch. Partial Differ. Equ. Anal. Comput., 7 (2019), 476-494. (See also arXiv:1710.09090[math.NA].)
  • Y. Nakano. Convergence of the meshfree collocation methods for fully nonlinear parabolic equations, Numer. Math., 136 (2017), 703-723. (See also arXiv:1408.5195 [math.NA].)
  • Y. Nakano. On quadratic approximations for Hamilton-Jacobi-Bellman equations, Automatica, 66 (2016), 205-217.
  • Y. Nakano. On a law of large numbers for insurance risks. arXiv:1601.03171[q-fin.RM].
  • Y. Nakano. On the design of catastrophe bonds, unpublished.
  • M. Ieda, T. Yamashita, and Y. Nakano. A liability tracking portfolio for pension fund management, Proceedings of the 46th ISCIE International Symposium on Stochastic Systems Theory and Its Applications, pp. 112-117, 2015.
  • A. Iizuka and Y. Nakano. On historical value-at-risk under distribution uncertainty, J. Math. Finance, 5 (2015), 113-118.
  • Y. Nakano. Quasi-Monte Carlo methods for Choquet integrals, J. Comput. Appl. Math., 287 (2015), 63-66.
  • Y. Nakano. An approximation scheme for stochastic controls in continuous time, Jpn. J. Ind. Appl. Math., 31 (2014), 681-696.
  • M. Ieda, T. Yamashita, and Y. Nakano. A liability tracking approach to long term management of pension funds, J. Math. Finance, 3 (2013), 392-400.
  • Y. Nakano. On approximating law-invariant comonotonic coherent risk measures, Astin Bulletin, 42 (2012), 343-353.
  • Y. Nakano. Partial hedging for defaultable claims, Adv. Math. Econ., 14 (2011), 127-145.
  • Y. Nakano. Quantile hedging for defaultable claims, Recent Advances in Financial Engineering: Proceedings of the KIER-TMU International Workshop on Financial Engineering 2009, World Scientific, 2010, 219-230.
  • K. Fukuda, A. Inoue, and Y. Nakano. Optimal intertemporal risk allocation applied to insurance pricing. arXiv:0711.1143[q-fin.PR].
  • K. Fukuda, A. Inoue, and Y. Nakano. Dynamic risk diversification and insurance premium principles. arXiv:1303.3956[math.PR].
  • K. Fukuda, A. Inoue, and Y. Nakano. Premium Calculation and Optimal Intertemporal Risk Diversification, RIMS Kôkyûroku, 1580 (2008), 150-162. (in Japanese)
  • A. Inoue and Y. Nakano. Remark on optimal investment in a market with memory, Theory of Stochastic Processes, 13 (2007), 66-76.
  • A. Inoue and Y. Nakano. Optimal long term investment model with memory, Appl. Math. Optim., 55 (2007), 93-122.
  • A. Inoue, Y. Nakano and V. Anh. Binary market models with memory, Statist. Probab. Lett., 77 (2007), 256-264.
  • Y. Nakano, Mean-risk optimization for index tracking, Statist. Decisions, 24 (2006), 189-207.
  • A. Inoue, Y. Nakano and V. Anh. Linear filtering of systems with memory and application to finance, J. Appl. Math. Stochastic Anal., (2006), Art. ID 53104, 26pp.
  • Y. Nakano. Minimization of shortfall risk in a jump-diffusion model, Statist. Probab. Lett., 67 (2004), 87-95.
  • Y. Nakano. Efficient hedging with coherent risk measure, J. Math. Anal. Appl., 293 (2004), 345-354.
  • Y. Nakano. Minimizing coherent risk measures of shortfall in discrete-time models under cone constraints, Appl. Math. Finance, 10 (2003), 163-181.
  • Y. Nakano. Optimal hedging in the presence of shortfall risk, Doctoral Dissertation, Hokkaido University, 2005.
Books
  • A. Inoue, Y. Nakano, and K. Fukuda, Mathematics of Finance and Insurance, Iwanami Shoten, 2014. (in Japanese)

Mathematics of Finance and Insurance - Iwanami Shoten

Lecture Notes
  • Introduction to Probability Theory

probab02.pdf

  • Introduction to Markov Processes

intro_markov_processes.pdf

  • Stochastic Differential Equations

sde09.pdf

Oral Presentations (2018-)
  • K. Watanabe, Portfolio optimization using randomized signatures, JSIAM 11th Student Research Presentation, March 12, 2025, The University of Tokyo. (in Japanese)
  • Y. Nakano, On the convergence of differentiable approximation schemes for Hamilton-Jacobi-Bellman equations, JSIAM 22nd Joint Workshop, March 9, 2026, The University of Tokyo. (in Japanese)
  • Y. Nakano, Error estimation of Denoising Diffusion Probabilistic Models, Symposium on Probability Theory 2025, December 17, 2025, Kumamoto University. (in Japanese)
  • Y. Nakano, On the convergence of differentiable approximation schemes for Hamilton-Jacobi-Bellman equations, 12th Workshop on Probability Theory and PDEs, November 22, 2025, Tsuda University. (in Japanese)
  • Y. Nakano, Convergence of differentiable approximation schemes for fully nonlinear parabolic equations, CJ Numerical PDEs, September 23, 2025, University of Electronic Science and Technology of China, Chengdu, China.
  • M. Ieda and Y. Nakano, On iterative methods for systems of linear equations appearing in RBF interpolation, JSIAM Annual Meeting 2025, September 4, 2025, Tokyo University of Science. (in Japanese)
  • Y. Nakano, Error estimation of Denoising Diffusion Probabilistic Models, JSIAM Annual Meeting 2025, September 4, 2025, Tokyo University of Science. (in Japanese)
  • Y. Nakano, On inverse problems for stochastic optimal controls, SIAM Conference on Control and Its Applications (CT25), July 29, 2025, Montréal Convention Center, Montréal, Canada.
  • T. Saito, Solving Monge problem by Hilbert space embeddings of probability measures, JSIAM 10th Student Research Presentation, March 8, 2025, Okayama International Center. (in Japanese)
  • T. Inoue, Deep hedging by Neural SDEs, JSIAM 10th Student Research Presentation, March 8, 2025, Okayama International Center. (in Japanese)
  • T. Saito and Y. Nakano, Solving Monge problem by Hilbert space embeddings of probability measures, 14th International Conference on Operations Research and Enterprise Systems, February 25, 2025, Vila Galé Porto, Porto, Portugal.
  • T. Saito and Y. Nakano, Solving Monge problem by Hilbert space embeddings of probability measures, Stochastic Optimal Transport and Related Topics 2025, January 12, 2025, Tsuda University, Tokyo, Japan.
  • Y. Nakano, Schrödinger’s problem and diffusion generative models, Stochastic Optimal Transport and Related Topics 2025, January 11, 2025, Tsuda University, Tokyo, Japan.
  • T. Saito and Y. Nakano, Approximate solution to Monge problem by Hilbert space embeddings of probability measures, The 56th ISCIE International Symposium on Stochastic Systems Theory and Its Applications (SSS'24), December 14, 2024, Maizuru Brick Park, Kyoto, Japan.
  • Y. Nakano, Schrödinger's problem and diffusion generative models, UTNAS, November 27, 2024, The University of Tokyo. (in Japanese)
  • Y. Nakano, On the convergence of diffusion models, JSIAM Annual Meeting 2024, September 14, 2024, Kyoto University. (in Japanese)
  • Y. Nakano, On the convergence of diffusion generative models, MSJ Autumn Meeting 2024, September 4, 2024, Osaka University. (in Japanese)
  • N. Iida, Application of regularity structure theory to HJM models, JSIAM 9th Student Research Presentation, March 7, 2024, Aore Nagaoka. (in Japanese)
  • K. Kyushima, A transient market impact model with stochastic structures, JSIAM 9th Student Research Presentation, March 7, 2024, Aore Nagaoka. (in Japanese)
  • T. Matsumaru, Neural SDE models using multiplex fractional Brownian motion, JSIAM 9th Student Research Presentation, March 7, 2024, Aore Nagaoka. (in Japanese)
  • Y. Nakano, A kernel-based method for Schrödinger bridges, 10th International Congress on Industrial and Applied Mathematics, August 23, 2023, Waseda University, Tokyo, Japan.
  • K. Kyushima, Numerical analysis of forward-backward stochastic differential equations with jumps using deep learning, JSIAM 19th Joint Workshop, March 9, 2023, Okayama University of Science (Hybrid). (in Japanese)
  • T. Bekki, Numerical analysis of Dynkin games using deep learning, JSIAM Annual Meeting 2022, September 10, 2022, Hokkaido University. (in Japanese)
  • K. Eto, On relative arbitrage using Lyapunov functions, JSIAM 18th Joint Workshop, March 9, 2022, Online. (in Japanese)
  • Y. Nakano, Inverse problems for continuous-time stochastic optimal controls, The 53rd ISCIE International Symposium on Stochastic Systems Theory and Its Applications, October 31, 2021, Ritsumeikan University, Shiga, Japan.
  • K. Endo and Y. Nakano, Numerical analysis of McKean-Vlasov type stochastic differential equations using function approximation, JSIAM Annual Meeting 2021, September 9, 2021, Online. (in Japanese)
  • K. Nakasa and Y. Nakano, Modeling of COVID-19 by stochastic differential equations and parameter estimation, JSIAM Annual Meeting 2021, September 9, 2021, Online. (in Japanese)
  • Y. Nakano, Inverse stochastic optimal controls, SIAM Conference on Control and Its Applications, July 21, 2021, Virtual Conference.
  • T. Miwa, Mathematical models of COVID-19 and stochastic control, JSIAM 6th Student Research Presentation, March 8, 2021, Online. (in Japanese)
  • T. Toyoshima and Y. Nakano, On the Heath-Jarrow-Morton-Musiela equation with boundary conditions driven by Lévy processes, MSJ Autumn Meeting 2019, September 18, 2019, Kanazawa University. (in Japanese)
  • Y. Nakano, On the convergence of kernel collocation methods for nonlinear parabolic PDEs, Foundations and Applications of Numerical Analysis Supporting Next-Generation Science and Technology, November 16, 2018, RIMS, Kyoto University. (in Japanese)
  • K. Kato, Stochastic optimal control in mathematical models of infectious diseases, JSIAM Annual Meeting 2018, September 5, 2018, Nagoya University. (in Japanese)
  • S. Tanaka, Numerical analysis of backward stochastic differential equations using reproducing kernel interpolation, JSIAM Annual Meeting 2018, September 4, 2018, Nagoya University. (in Japanese)
  • Y. Nakano, Convergent collocation methods for fully nonlinear parabolic equations, CJK Conference on Numerical Mathematics 2018, August 22, 2018, Shiinoki Cultural Complex, Kanazawa, Japan.
  • Y. Nakano, Convergent collocation methods for Hamilton-Jacobi-Bellman equations, The 23rd International Symposium on Mathematical Theory of Networks and Systems, July 20, 2018, The Hong Kong University of Science and Technology, Hong Kong, China.
Theses (2018-)
  • A. Mori, Verification of implied volatility error using the stochastic local volatility framework, Master's Thesis, AY 2025. (in Japanese)
  • K. Watanabe, Portfolio optimization using randomized signatures, Master's Thesis, AY 2025. (in Japanese)
  • T. Inoue, Deep hedging by Neural SDEs, Master's Thesis, AY 2024. (in Japanese)
  • R. Otaki, Prediction of local volatility by machine learning, Master's Thesis, AY 2024. (in Japanese)
  • R. Ono, Construction of arbitrage-free volatility surfaces, Master's Thesis, AY 2024. (in Japanese)
  • Y. Kawano, Deep calibration for the Cox-Ingersoll-Ross model, Master's Thesis, AY 2024. (in Japanese)
  • R. Hirata, Monte Carlo methods using Neural-Schrödinger-Föllmer diffusion, Bachelor's Thesis, AY 2024. (in Japanese)
  • N. Iida, Application of rough path theory to HJM models, Master's Thesis, AY 2023. (in Japanese)
  • K. Kyushima, A transient market impact model with stochastic structures, Master's Thesis, AY 2023. (in Japanese)
  • T. Bekki, Generative models for distributional interpolation, Master's Thesis, AY 2023. (in Japanese)
  • T. Matsumaru, Proposal of Neural SDE models using multiplex fractional Brownian motion, Master's Thesis, AY 2023. (in Japanese)
  • T. Kaneko, Deep learning-based stochastic volatility models with consistency to volatility index, Bachelor's Thesis, AY 2023. (in Japanese)
  • K. Endo, Monte Carlo methods using Schrödinger-Föllmer diffusion, Master's Thesis, AY 2022. (in Japanese)
  • K. Nakasa, Parameter estimation of COVID-19 infection models by particle filters, Master's Thesis, AY 2022. (in Japanese)
  • K. Daikuya, Stochastic volatility models with uniform distribution, Bachelor's Thesis, AY 2022. (in Japanese)
  • K. Eto, Optimization of Lyapunov functions in stochastic portfolio theory, Master's Thesis, AY 2021. (in Japanese)
  • T. Takahashi, XVA for path-dependent options based on arbitrage-free pricing theory and its numerical analysis, Master's Thesis, AY 2021. (in Japanese)
  • T. Toyoshima, Fractional stochastic Navier-Stokes equations driven by space-time white noise, Master's Thesis, AY 2021. (in Japanese)
  • K. Kyushima, Numerical analysis of forward-backward stochastic differential equations with jumps using deep learning, Bachelor's Thesis, AY 2021. (in Japanese)
  • T. Bekki, Numerical analysis of game options using deep learning, Bachelor's Thesis, AY 2021. (in Japanese)
  • T. Matsumaru, Numerical solution of stochastic differential equations using generative adversarial networks, Bachelor's Thesis, AY 2021. (in Japanese)
  • K. Takagi, Estimation of the SABR-HW model using the Kushner-Stratonovich equation with reproducing kernel interpolation, Master's Thesis, AY 2020. (in Japanese)
  • H. Takamine, Application of high-order discretization schemes to American option pricing using forward-backward stochastic differential equations, Master's Thesis, AY 2020. (in Japanese)
  • T. Miwa, Mathematical models of COVID-19 and stochastic control, Master's Thesis, AY 2020. (in Japanese)
  • K. Endo, Numerical analysis of McKean-Vlasov type stochastic differential equations using function approximation, Bachelor's Thesis, AY 2020. (in Japanese)
  • K. Nakasa, Modeling of COVID-19 by stochastic differential equations, Bachelor's Thesis, AY 2020. (in Japanese)
  • K. Kato, Stochastic optimal control in mathematical models of Ebola virus disease, Master's Thesis, AY 2019. (in Japanese)
  • S. Tanaka, Numerical analysis of backward stochastic differential equations using reproducing kernel approximation with regularization, Master's Thesis, AY 2019. (in Japanese)
  • Yuda Nie, Deep learning in stochastic portfolio theory, Master's Thesis, AY 2019.
  • T. Takahashi, Numerical analysis of XVA for path-dependent options using branching processes, Bachelor's Thesis, AY 2019. (in Japanese)
  • Y. Kinoshita, Calibration methods using stochastic gradient descent, Master's Thesis, AY 2018. (in Japanese)
  • K. Kurihara, Robust asset management under uncertain drift and volatility, Master's Thesis, AY 2018. (in Japanese)
  • H. Noda, Optimal liquidation problems for liabilities considering market impact, Master's Thesis, AY 2018. (in Japanese)
  • K. Takagi, Estimation of the term structure of interest rates using reproducing kernel interpolation by Zakai equations, Bachelor's Thesis, AY 2018. (in Japanese)
  • T. Toyoshima, Unique existence of weak solutions for the Heath-Jarrow-Morton-Musiela equation under boundary conditions, Bachelor's Thesis, AY 2018. (in Japanese)
  • T. Miwa, Mathematical models of schistosomiasis and stochastic control, Bachelor's Thesis, AY 2018. (in Japanese)