Le Laboratoire de Probabilité
ArXiv I'm Takahiro Tsuchiya (土屋貴裕) , Associate Professor at the University of Aizu.
My main area of research is forward-backward stochastic differential equations (FBSDEs), in particular methods for numerical theory and calculation of FBSDEs which appear in financial mathematics or the applications.
Research interests
Forward-backward stochastic differential equations (FBSDEs), Theory of computation of (FB)SDEs and the applications. In particular, machine learning and Stochastic Differential Equations.
Current Research
Published papers
Fully coupled drift-less Forard and backward Stochastic Differential Equations in a degenerate case, Journal of Industrial and Applied Mathematics volume 40, pages 1031–1051 (2023), https://arxiv.org/abs/2112.12257
Newton-Kantorovitch method for decoupled forward-backward stochastic differential equations, (with Dai Tagichi), Vol. 2021 (2021), No. 98, pp. 1-16.
Stability problems for Cantor stochastic differential equations, (with Hiroya Hashimoto), Stochastic Processes and their Applications, Volume 128, Issue 1, January 2018, Pages 211-232 (ArXiv), https://doi.org/10.1016/j.spa.2017.04.008
A Heat Kernel Approach to Interest Rate Models, (with Jiro Akahori, Yuji Hishida, and Josef Teichmann), Japan Journal of Industrial and Applied Mathematics June 2014, Volume 31, Issue 2, pp 419-439 (ArXiv), https://doi.org/10.1007/s13160-014-0147-3
Remarks on the rate of strong convergence of Euler-Maruyama approximation for SDEs driven by rotation invariant stable processes, (with Hiroya Hashimoto), JSIAM Letters, 5:13–16, 2013, https://doi.org/10.14495/jsiaml.5.13
Defaultable bonds via HKA, (with Yuta Inoue), International Journal of Innovative Computing, Information and Control., 8(3 (B)):2225–2231, March 2012,ArXiv, http://www.ijicic.org/sss10-05.pdf
On the pathwise uniqueness of solutions of stochastic differential equations driven by multi-dimensional symmetric α stable class, J. Math. Kyoto Univ., 46(1):107–121, 2006. https://projecteuclid.org/euclid.kjm/1250281799
What is the natural scale for a L’evy process in modelling term structure of interest rates?, (with Jiro Akahori), Asia-Pacific Financial Markets, 13(4):299–313, 2006 (ArXiv), https://doi.org/10.1007/s10690-007-9046-9
On stochastic differential equations driven by symmetric stable processes of index α, (with Hashimoto Hiroya and Yadama Toshio), Shinzo Watanabe et al., Stochastic processes and applications to mathematical finance. Proceedings of the 5th Ritsumeikan international symposium, Kyoto, Japan, March 3--6, 2005. Hackensack, NJ: World Scientific. 183-193 (2006), https://doi.org/10.1142/9789812774637_0006
Forward-backward stochastic differential equations and Newton’s method, in Japanese, RIMS Kokyuroku, 2116-16, 2018.
On the convergent rates of Euler-Maruyama schemes for SDEs driven by rotation invariant α-stable processes, (with Hiroya Hashimoto) in Japanese, RIMS Kokyuroku, 229-236, 2013
How does a Hot Spot come into existence? Remarks on Simulation of Radiation Diffusion, (with Nobutaka Shimizu), Proceedings of the 44th ISCIE International Symposium on Stochastic Systems Theory and Its Applications Tokyo, Japan, November 1-2, 2013. https://doi.org/10.5687/sss.2013.307
HKA to single defaultable bond, (with Yuta Inoue), Proceedings of the 42nd ISCIE international symposium on stochastic systems theory and its applications, Okayama, Japan, November 26–27, 2010. Kyoto: The Institute of Systems, Control and Information Engineers (ISCIE), pages 96–101, 2011. https://doi.org/10.5687/sss.2011.96
An introduction to Neural Stochastic Differential Equations, The 52nd ISCIE International Symposium on Stochastic Systems Theory and Its Applications (SSS '20), 10.30.2021.
退化する係数をもつ FBSDE の解の存在と一意性について，岡山 確率解析ワークショップ 2022, 02.21.2021.
Forward-Backward stochastic differential equations and Newton's method, 18.03.2019 日本数学会 2019年度年会
Newton method and Backward Stochastic (differential) equations,福岡大学確率論セミナー， 27.12.2018
FBSDEsとニュートン近似，確率論シンポジウム，京都大学数理解析研究所420号室，10:50--11:30．予稿pdf. 19.12.2018.
カントール拡散過程の安定性問題とその応用， 仙台市青葉区片平二丁目1-1 東北大学片平キャンパス さくらホール，12/12 2017 15:30 - 16:00
局所的にヘルダー連続な拡散係数を持つカントール確率微分方程式について，立命館大学びわこ・くさつキャンパス(BKC) ウェストウィング6階談話会室 日時： 2017年11月30日（木）16:30-18:45
Stability problems for Cantor stochastic differential equations, 福岡大学理学部9号館4階大学院講義室3，2017年11月2日 16:30-18:00．
「カントール関数を拡散係数にもつ SDE と 一般化された中尾-Le Gall 条件」，日本数学会2016年度秋季総合分科会，関西大学千里山キャンパス，09.15.2016, 講演pdf, 予稿pdf. The related research paper is available at (ArXiv).
A note of Newton's method on SDEs with unbounded coefficients, The 47th ISCIE International Symposium on Stochastic Systems Theory and Its Applications, Waikiki Beach Marriott Resort & Spa, Honolulu, Hawaii, USA, 07.12.2015,
On the convergent rates of Euler-Maruyama schemes for SDEs driven by rotation invariant α-stable processes, in Japanese, RIMS Workshop: Probability Symposium, 21.12.2012
The convergence rate of Euler-Maruyama approximation for SDEs driven by symmetric stable processes, JSIAM Mathematical Finance seminar, 15.09.2012.
(Invited speaker) Heat kernel approach and its applications in finance, Third Florence-Ritsumeikan Workshop on Probability and Finance. University of Florence, Italy, 16.03.2011.
(Invited speaker) Heat Kernel Approach to modeling of Defaultable Markets, Seminar of Universite degli Studi di Padova Dipartimento di Matematica Pura ed Applicata. Padova University, Italy, 14.03.2011.
(Invited speaker) Heat kernel approach in finance and its applications, Mathematical finance seminars of the Department of Mathematics of Imperial College London, Imperial College London, England 09.03.2011
The Defaultable Market via HKA, the 42nd ISCIE International Symposium on Stochastic Systems Theory and Its Applications.. 26.11.2011.
A Heat Kernel Approach to Interest Rate Models, Workshop Finance and Insurance, Jena in Germany. 16.03.2009.
On a multi-dimensional extension of the Komatsu-Yamada-Watanabe condition, Poster session of Fourth World Congress Bachelier Finance Society 2006.
Patents
2012年 会津大学 競争的研究費``Analysis the diffusion of the radioactive substance"
2011年 立命館大学「東日本大震災に関る研究推進プログラム」
2011年 JST戦略的創造研究推進事業 （受付番号 C 共 -036 ）
2007年 JSPS科学研究費補助金 (特別研究員奨励費).
研究の紹介(A Test (heavy...) page via iCloud pages)