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Study on nonlinear problems arising in mathematical finance

Research Project

Project/Area Number 20K03737
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionChuo University

Principal Investigator

Ishimura Naoyuki  中央大学, 商学部, 教授 (80212934)

Project Period (FY) 2020-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2023: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords数理ファイナンス / リスク指標 / コピュラ / Value at Risk / 破産確率 / 積分方程式 / 数値解法 / スペクトル選点法 / コピュラ(接合関数) / 非線形問題 / VaR / 最適投資問題
Outline of Research at the Start

数理ファイナンスに現れる非線形問題の解法を,応用解析の手法を用いて研究する。特に
(1) コピュラを用いた非線形関係の研究:時間発展およびVaRとの関連
(2) 最適投資問題に現れる特異な非線形偏微分および離散方程式の研究
の2つの課題を中心に,数理ファイナンスに現れる非線形問題の解析を行い,問題に含まれているリスクとその評価,それらの解析を通して,応用解析の手法が,広く数理科学一般に貢献することを明らかにする。

Outline of Final Research Achievements

We introduce a new risk indicator, which involves nonlinear relations. In particular, we introduce a new concept of copula-based Value at Risk in the form of ready to handle. Collaboration with Dr Andres Mauricio Molina Barreto, our new indicator can be applied successfully to real data.
In the study of numerical computation of the integral equation for the ruin probability, we employ the bounding transformation with a spectral collocation method and as a result we are able to present an efficient numerical procedure. For several important relevant distributions, our method is shown to work effectively.

Academic Significance and Societal Importance of the Research Achievements

リスク指標の研究では,非線形性な相関を記述することが可能でありつつ扱いも簡便な新たな指標を導入することに成功した。リスク管理の観点からも利用ができるものであり,そのため実用上も意義があると考えている。破産確率の数値解法の研究では,無限区間を有限区間に変換する手法は他の方程式に関しても有効である。誤差の一つを回避する手法の成功例として,他の方程式への適用を示唆する研究成果として学術的に意味があると考える。

Report

(5 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (16 results)

All 2024 2023 2022 2021 2020 Other

All Journal Article (9 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 8 results,  Open Access: 8 results) Presentation (5 results) (of which Int'l Joint Research: 5 results,  Invited: 3 results) Remarks (2 results)

  • [Journal Article] Efficient numerical computation of the ruin probability2023

    • Author(s)
      Soutome Hiroko、Ishimura Naoyuki、Imai Hitoshi
    • Journal Title

      Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications

      Volume: 2023 Issue: 0 Pages: 35-40

    • DOI

      10.5687/sss.2023.35

    • ISSN
      2188-4730, 2188-4749
    • Year and Date
      2023-03-24
    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Remarks on a copula‐based conditional value at risk for the portfolio problem2023

    • Author(s)
      Molina Barreto Andres Mauricio、Ishimura Naoyuki
    • Journal Title

      Intelligent Systems in Accounting, Finance and Management

      Volume: 30 Issue: 3 Pages: 150-170

    • DOI

      10.1002/isaf.1540

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Efficient Numerical Computation of the Integral Equation for the Ruin Probability2023

    • Author(s)
      Soutome Hiroko、Ishimura Naoyuki、Imai Hitoshi
    • Journal Title

      IEEE XPlore: 2023 27th International Computer Science and Engineering Conference (ICSEC)

      Volume: 2023 Pages: 37

    • DOI

      10.1109/icsec59635.2023.10329787

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Efficient numerical computation of the ruin probability2023

    • Author(s)
      Hiroko Soutome, Naoyuki Ishimura, Hitoshi Imai
    • Journal Title

      Proceedings of the 54th ISCIE International Symposium on Stochastic Systems Theory and Its Applications Nara, Oct. 14-15, 2022

      Volume: 54 Pages: 3540-3540

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Global in space numerical computation of the ruin probability2022

    • Author(s)
      Hiroko Soutome, Naoyuki Ishimura, Hitoshi Imai
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: 31 Pages: 397406-397406

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] On a determination formula for the estimation of copula-based Value at Risk2022

    • Author(s)
      Andres Mauricio Molina Barreto, Naoyuki Ishimura, and Koichiro Takaoka
    • Journal Title

      Proceedings of the 53rd International Symposium on Stochastic Systems Theory and its Applications, https://www.jstage.jst.go.jp/browse/sss/-char/en

      Volume: 2022 Pages: 86-92

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Copula-based estimation of Value at Risk for the portfolio problem2021

    • Author(s)
      Andres Mauricio Molina Barreto and Naoyuki Ishimura
    • Journal Title

      Proceedings of the Forum "Math-for-Industry" 2018 (Cheng J., Dinghua X., Saeki O., Shirai T. (eds))

      Volume: 35 Pages: 1-13

    • DOI

      10.1007/978-981-16-5576-0_1

    • ISBN
      9789811655753, 9789811655760
    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A determination formula on the copula-based estimation of Value at Risk for the portfolio problem2020

    • Author(s)
      Andres Mauricio Molina Barreto and Naoyuki Ishimura
    • Journal Title

      Proceedings of RSU International Research Conference 2020

      Volume: 6 Pages: 1236-1246

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Risk calculating for financial institutions2020

    • Author(s)
      Naoyuki Ishimura
    • Journal Title

      Impact, www.impact.pub

      Volume: December Pages: 48-50

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Presentation] Global in space numerical computation of the integral equations with application to the ruin probability2024

    • Author(s)
      Naoyuki Ishimura
    • Organizer
      16th International Conference on Computer Research and Development (ICCRD)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Insurance design for epidemic outbreaks involving Cramer-Lundberg model2024

    • Author(s)
      Naoyuki Ishimura
    • Organizer
      International Conference on Computational Finance (ICCF24)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Efficient numerical scheme of the integral equations with application to the ruin probability2023

    • Author(s)
      Naoyuki Ishimura
    • Organizer
      The 13th International Conference on Applied Physics and Mathematics (Singapore)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Efficient numerical computation of the ruin probability2022

    • Author(s)
      Naoyuki Ishimura
    • Organizer
      5th European Actuarial Journal Conference (Tartu, Estonia)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] On a determination formula for the estimation of copula-based Value at Risk2022

    • Author(s)
      Naoyuki Ishimura
    • Organizer
      12th International Conference on Applied Physics and Mathematics
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] 中央大学 研究者情報データベース

    • URL

      https://c-research.chuo-u.ac.jp/html/100003011_ja.html

    • Related Report
      2023 Annual Research Report
  • [Remarks] 中央大学研究者情報データベース

    • URL

      https://c-research.chuo-u.ac.jp/html/100003011_ja.html

    • Related Report
      2022 Research-status Report

URL: 

Published: 2020-04-28   Modified: 2025-01-30  

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