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Heat Kernel Approach in Financial Engineering of New Generation

Research Project

Project/Area Number 25285102
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Money/ Finance
Research InstitutionRitsumeikan University

Principal Investigator

Akahori Jiro  立命館大学, 理工学部, 教授 (50309100)

Co-Investigator(Kenkyū-buntansha) 堀 敬一  関西学院大学, 経済学部, 教授 (50273561)
Kohatsu・Higa A  立命館大学, 理工学部, 教授 (80420412)
足立 高徳  立命館大学, BKC社系研究機構, 教授 (60733722)
今村 悠里  立命館大学, 理工学部, 助教 (40633194)
劉 念麟  立命館大学, 総合科学技術研究機構, 研究員 (90610923)
Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥16,900,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥3,900,000)
Fiscal Year 2017: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2016: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2015: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Keywords数理ファイナンス / フーリエ法 / タイミングリスク / 静的ヘッジ / フラクショナルボラティリティ / 連続時間マクロファイナンス / ラフボラティリティモデル / 連鎖倒産モデル / 拡散過程の対称化 / 確率論 / 金融論 / 応用数学 / 熱核法 / 構造型アプローチ / 国際研究者交流 / 国際情報交換 / 金利の期間構造 / エキゾチックデリバティブ
Outline of Final Research Achievements

The project contributed, from the perspective of stochastic calculus, to the new developments in the field of financial engineering after the financial crisis. In the new generation modelling, more sophisticated theoretical foundations
explaining interactions among the various models are required, compared with the old type ones where in most parts the modelling was ad-hoc. This project promoted good many fruitful international research collaborations.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • Research Products

    (60 results)

All 2018 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (15 results) Journal Article (16 results) (of which Int'l Joint Research: 6 results,  Open Access: 8 results,  Peer Reviewed: 14 results,  Acknowledgement Compliant: 6 results) Presentation (21 results) (of which Int'l Joint Research: 6 results,  Invited: 17 results) Remarks (3 results) Funded Workshop (5 results)

  • [Int'l Joint Research] University of Verona/University of Parma/University of Florence(Italy)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] University of Liverpool/London School of Economics(United Kingdom)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] City University of New York/Drexel University(米国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Hochiminh University(ベトナム)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Monash University(Australia)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] University of Liverpool/University College, London/London School of Economics(United Kingdom)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] New York City University/University of Cincinnati/Michigan University(米国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] University of Florence/University of Parma/Scuola Normale di Pisa(Italy)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] ESSEC(France)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research]

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] フィレンツェ大学/パルマ大学(イタリア)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] リバプール大学(英国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] ミシガン大学(米国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] チューリッヒ連邦工科大チューリッヒ校(スイス)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] モナッシュ大学(オーストラリア)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Asymptotic Static Hedge via Symmetrization2018

    • Author(s)
      J. Akahori, Barsotti, F., & Imamura, Y.
    • Journal Title

      arXiv

      Volume: arXiv:1801.04045 [q-fin.PR]

    • Related Report
      2017 Annual Research Report
    • Open Access / Int'l Joint Research
  • [Journal Article] Default Contagion with Domino Effect, A First Passage Time Approach2017

    • Author(s)
      Jiro Akahori, Hai Ha Pham
    • Journal Title

      arXiv

      Volume: arXiv:1708.08411 [q-fin.MF]

    • Related Report
      2017 Annual Research Report
    • Open Access / Int'l Joint Research
  • [Journal Article] The Value of Timing Risk2017

    • Author(s)
      Jiro Akahori, Flavia Barsotti, Yuri Imamura
    • Journal Title

      arXiv:1701.05695

      Volume: NA

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Probability density of lognormal fractional SABR model2017

    • Author(s)
      Jiro Akahori, Xiaoming Song, Tai-Ho Wang
    • Journal Title

      arXiv:1702.08081

      Volume: NA

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A Discrete-Time Clark-Ocone Formula and its Application to an Error Analysis2016

    • Author(s)
      Jiro Akahori, Takafumi Amaba, Kaori Okuma
    • Journal Title

      Journal of Theoretical Probability

      Volume: published online Issue: 3 Pages: 932-960

    • DOI

      10.1007/s10959-016-0666-8

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Attraction properties for general urn processes and applications to a class of interacting reinforced particle systems2016

    • Author(s)
      Jiro Akahori, Andrea Collevecchio, Timothy Garoni, Kais Hamza
    • Journal Title

      arXiv:1602.05677

      Volume: NA

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Bridge representation and modal-path approximation2016

    • Author(s)
      Jiro Akahori, Xiaoming Song, Tai-Ho Wang
    • Journal Title

      arXiv:1607.03074

      Volume: NA

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Affine term structure as multi-soliton2014

    • Author(s)
      Hidemi Aihara, Jiro Akahori, and Edouard Grenier
    • Journal Title

      JSIAM Letters

      Volume: 6 Issue: 0 Pages: 17-20

    • DOI

      10.14495/jsiaml.6.17

    • NAID

      130004540626

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2014 Annual Research Report 2013 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A Heat Kernel Approach to Interest Rate Models2014

    • Author(s)
      Jiro Akahori, Yuji Hishida, Josef Teichmann and Takahiro Tsuchiya
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 31/2 Issue: 2 Pages: 419-439

    • DOI

      10.1007/s13160-014-0147-3

    • Related Report
      2014 Annual Research Report 2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some results on Parisian walks2014

    • Author(s)
      J. Akahori and Y. Ida
    • Journal Title

      JSIAM Letters

      Volume: 6 Issue: 0 Pages: 77-80

    • DOI

      10.14495/jsiaml.6.77

    • NAID

      130004706461

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On a symmetrization of diffusion processes2014

    • Author(s)
      Jiro Akahori and Yuri Imamura
    • Journal Title

      Quantitative Finance

      Volume: 印刷中 Issue: 7 Pages: 1211-1216

    • DOI

      10.1080/14697688.2013.825923

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Investment Timing Decisions of Managers under Endogenous Contracts2014

    • Author(s)
      Keiichi Hori and Hiroshi Osano
    • Journal Title

      Journal of Corporate Finance

      Volume: 29 Pages: 607-627

    • DOI

      10.1016/j.jcorpfin.2013.11.013

    • NAID

      120005525706

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tau functions of KP solitons realized in Wiener space2013

    • Author(s)
      Hidemi Aihara, Jiro Akahori, Hiroko Fujii, Yasuhumi Nitta
    • Journal Title

      Bulletin of the London Mathematical Society

      Volume: 45/6 Issue: 6 Pages: 1301-1309

    • DOI

      10.1112/blms/bdt056

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An Algebraic Approach to the Cameron-Martin-Maruyama-Girsanov Formula2013

    • Author(s)
      Jiro Akahori, Takafumi Amaba, Sachiyo Uraguchi
    • Journal Title

      Mathematical Journal of Okayama University

      Volume: 55 Pages: 167-190

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Managerial Incentives and the Role of Advisors in the Continuous-Time Agency Model2013

    • Author(s)
      Keiichi Hori and Hiroshi Osano
    • Journal Title

      Review of Financial Studies

      Volume: 26/ 10 Issue: 10 Pages: 2620-2647

    • DOI

      10.1093/rfs/hht027

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion2013

    • Author(s)
      Yuri Imamura, Katsuya Takagi
    • Journal Title

      Asia-Pacific Financial Markets

      Volume: 20 Issue: 1 Pages: 71-81

    • DOI

      10.1007/s10690-012-9159-7

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Presentation] Stochastic Calculus of General Equilibrium2018

    • Author(s)
      Jiro Akahori
    • Organizer
      Workshop on Stochastic Control and Related Issues
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] An Order-1 Markov Chain Approximation of Symmetrized Diffusion Processes2017

    • Author(s)
      Jiro Akahori
    • Organizer
      Osaka-UCL Workshop on Stochastics, Numerics and Risk
    • Place of Presentation
      Osaka, Japan
    • Year and Date
      2017-03-30
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stochastic Volatility Models of Quadratic Volterra Gaussian Type2017

    • Author(s)
      Jiro Akahori
    • Organizer
      金融工学・数理計量ファイナンスの諸問題 2017
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Supersymmetry in Wiener Space2017

    • Author(s)
      Jiro Akahori
    • Organizer
      Stochastic Analysis and Related Fields
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] A Structural Model for Default Contagion2017

    • Author(s)
      Jiro Akahori
    • Organizer
      The Fifth Asian Quantitative Finance Conference
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Some Results on Fractional Brownian Motions2016

    • Author(s)
      Jiro Akahori
    • Organizer
      Sookmyung Women's University Financial Mathematics Seminar
    • Place of Presentation
      Seoul, Korea
    • Year and Date
      2016-12-09
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Probabilistic Representation of Tau Functions2016

    • Author(s)
      Jiro Akahori
    • Organizer
      Workshop on SDEs and Stochastic Processes
    • Place of Presentation
      Tianjin, China
    • Year and Date
      2016-04-28
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Hedging Error as a Timing Risk and its Static Hedge2015

    • Author(s)
      J. Akahori
    • Organizer
      Columbia-JAFEE Conference 2015
    • Place of Presentation
      NEW YORK(USA)
    • Year and Date
      2015-10-02
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Asymptotic and Exact Semi-Static Hedges of Barrier Options2015

    • Author(s)
      J.Akahori
    • Organizer
      The Third Asian Quantitative Finance Conference
    • Place of Presentation
      HONG KONG(P.R.CHINA)
    • Year and Date
      2015-07-07
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Statistical Estimation of Diffusion Processes2015

    • Author(s)
      J. Akahori
    • Organizer
      5th Ritsumeikan-Monash Symposium on Probability and Related Fields
    • Place of Presentation
      Melbourne(Australia)
    • Year and Date
      2015-03-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Asymptotic and Exact Semi-Static Hedges2015

    • Author(s)
      J. Akahori
    • Organizer
      WORKSHOP ON "MATHEMATICAL FINANCE AND RELATED ISSUES"
    • Place of Presentation
      大阪大学(大阪府)
    • Year and Date
      2015-03-16
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On a Generalization of Malliavin-Mancino's Fourier Estimation Method2014

    • Author(s)
      J.Akahori
    • Organizer
      The Quantitative Methods in Finance 2014 Conference
    • Place of Presentation
      Sydney(Australia)
    • Year and Date
      2014-12-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Fourier estimation method with positive semi-definite estimators2014

    • Author(s)
      J.Akahori
    • Organizer
      The 8th International Conference on Computational and Financial Econometrics
    • Place of Presentation
      Pisa(Italy)
    • Year and Date
      2014-12-08
    • Related Report
      2014 Annual Research Report
  • [Presentation] Parametrix of Static Hedge (of a Timing Risk)2014

    • Author(s)
      J. Akahori
    • Organizer
      2014 Actuarial Teachers' and Researchers' Conference
    • Place of Presentation
      Edinburgh(Scotland)
    • Year and Date
      2014-12-01
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On a Generalization of Malliavin-Mancino's Fourier Estimation Method2014

    • Author(s)
      J. Akahori
    • Organizer
      NUS-UTokyo Workshop on Quantitative Finance
    • Place of Presentation
      東京大学(東京都)
    • Year and Date
      2014-09-26
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] A multi-period coherent risk measure defined in terms of sample quantiles2014

    • Author(s)
      J.Akahori
    • Organizer
      International Workshop on Risk Analysis, Ruin and Extremes
    • Place of Presentation
      天津(中華人民共和国)
    • Year and Date
      2014-07-14
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] A Modification of the Fourier Method

    • Author(s)
      J.Akahori
    • Organizer
      Stochastic Processes and Mathematical Finance
    • Place of Presentation
      関西大学(大阪府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Algebraic proof of anticipative Girsanov-Maruyama formula

    • Author(s)
      J. Akahori
    • Organizer
      The First International Workshop on Quantum Information Theory and Related Topics
    • Place of Presentation
      Danang, Vietnam
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] A Continuous-Time Agency Model under Loss Aversion

    • Author(s)
      K. Hori
    • Organizer
      67th European Meeting of the Econometric Society
    • Place of Presentation
      Gothenberg, Sweden
    • Related Report
      2013 Annual Research Report
  • [Presentation] An Asymptotic Static Hedge of a Timing Risk and its Error

    • Author(s)
      Y. Imamura
    • Organizer
      Stochastic processes and their statistics in Finance in Okinawa
    • Place of Presentation
      沖縄青年会館(沖縄県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Static hedging of timing risk

    • Author(s)
      Y. Imamura
    • Organizer
      The First International Workshop on Quantum Information Theory and Related Topics
    • Place of Presentation
      Danang, Vietnam
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Remarks] research-db

    • URL

      http://research-db.ritsumei.ac.jp/Profiles/38/0003770/prof_e.html

    • Related Report
      2013 Annual Research Report
  • [Remarks] research-db

    • URL

      http://research-db.ritsumei.ac.jp/Profiles/38/0003725/profile.html

    • Related Report
      2013 Annual Research Report
  • [Remarks] research-db

    • URL

      http://research-db.ritsumei.ac.jp/Profiles/102/0010172/profile.html

    • Related Report
      2013 Annual Research Report
  • [Funded Workshop] Mathematical Finance and Related Issues2018

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] 6th Ritsumeikan-Monash Symposium on Probability and Related Fields2016

    • Place of Presentation
      Ritsumeikan University, Biwako-Kusatsu Campus & Kansai University, Senri-Yama Campus
    • Year and Date
      2016-11-11
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Brownian Motion and Stochastic Processes2016

    • Place of Presentation
      Ritsumeikan University, Biwako-Kusatsu Campus
    • Year and Date
      2016-06-03
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] One day workshop on Stochastic Processes and Financial and Insurance Mathematics2016

    • Place of Presentation
      Ritsumeikan University, Biwako-Kusatsu Campus
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] One day workshop on Stochastic Processes and Financial and Insurance Mathematics II2016

    • Place of Presentation
      Ritsumeikan University, Biwako-Kusatsu Campus
    • Related Report
      2016 Annual Research Report

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Published: 2013-05-21   Modified: 2022-02-22  

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