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Efficient numerical methods in the computational finance

Research Project

Project/Area Number 21710157
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Social systems engineering/Safety system
Research InstitutionKeio University

Principal Investigator

IMAI Junichi  慶應義塾大学, 理工学部, 准教授 (10293078)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsファイナンス / 準モンテカルロ法 / シミュレーション工学 / 金融工学 / 数理工学 / レヴィ過程
Research Abstract

In this research project, I have proposed so called "Generalized Linear Transformation Method" that is proposed under Levy models. To be explicit, we develop new methods that are based on the explicit form of probability density function, series representation of the infinitely divisible distribution, using inverse Levy measure method, and using characteristic functions via discrete Fourier transformation. These methods enables us enhance the numerical efficiency of QMC method by minimizing the effective dimensions of the problems.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (34 results)

All 2012 2011 2010 2009 Other

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (16 results) Remarks (4 results)

  • [Journal Article] On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws2012

    • Author(s)
      Reiichiro Kawai, Junichi Imai
    • Journal Title

      Monte Carlo and Quasi-Monte Carlo Methods 2010

      Volume: (掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] ゲーム理論的リアルオプションアプローチによる中小企業と大企業の特許権取得競争分析2011

    • Author(s)
      青木, 今井
    • Journal Title

      リアルオプション研究

      Volume: 4(2) Pages: 169-206

    • NAID

      130001064984

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] フランチャイズビジネスにおける最適契約~商品の廃棄を考慮したロイヤルティ形態の比較~2011

    • Author(s)
      川地, 今井
    • Journal Title

      リアルオプション研究

      Volume: 4(1) Pages: 1-32

    • NAID

      130000670598

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws2011

    • Author(s)
      R. Kawai and J. Imai
    • Journal Title

      Monte Carlo and Quasi-Monte Carlo Methods 2010

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On finite truncation of infinite shot noise series representation of tempered stable laws2011

    • Author(s)
      J. Imai and R. Kawai
    • Journal Title

      Physica A : Statistical Mechanics and Applications

      Volume: 390(23-24) Pages: 4411-4425

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quasi-Monte Carlo method for infinitely divisible random vectors via series representations2010

    • Author(s)
      J. Imai and R. Kawai
    • Journal Title

      SIAM Journal on Scientific Computing

      Volume: 32 Pages: 265-275

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] マルコフ完全均衡と離散選択モデルを用いたイノベーションのジレンマの分析2009

    • Author(s)
      今井
    • Journal Title

      リアルオプション研究

      Volume: 2 Pages: 151-172

    • NAID

      130000149540

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dimension Reduction Approach To Simulating Exotic Options In A Meixner Levy Market2009

    • Author(s)
      J. Imai and K. S. Tan
    • Journal Title

      IAENG International Journal of Applied Mathematics

      Volume: 39(4) Pages: 265-275

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Generalized Linear Transformation Method for Simulating Meixner Levy Process2009

    • Author(s)
      J. Imai and K. S. Tan
    • Journal Title

      Proceedings of the World Congress on Engineering 2009

      Volume: II Pages: 1406-1411

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] An accelerating quasi-Monte Carlo method for option pricing under the generalized hyperbolic Levy process2009

    • Author(s)
      J. Imai and K. S. Tan
    • Journal Title

      SIAM Journal on Scientific Computing

      Volume: 31(3) Pages: 2282-2302

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] An accelerating quasi-Monte Carlo method for option pricing under the generalized hyper bolic Le'vy process2009

    • Author(s)
      J.Imai, K.S.Tan
    • Journal Title

      SIAM Journal on Scientific Computing 31(3)

      Pages: 2282-2302

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Generalized Linear Transformation Method for Simulating Meixner Levy Process2009

    • Author(s)
      J.Imai, K.S.Tan
    • Journal Title

      proceedings of the World Congress on Engineering 2009 II

      Pages: 1406-1411

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dimension Reduction Approach To Simulating Exotic Options In A Meixner Levy Market2009

    • Author(s)
      J.Imai, K.S.Tan
    • Journal Title

      IAENG International Journal of Applied Mathematics 39(4)

      Pages: 265-275

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] マルコフ完全均衡と離散選択モデルを用いたイノベーションのジレンマの分析2009

    • Author(s)
      今井潤一
    • Journal Title

      リアルオプション研究 2

      Pages: 151-172

    • NAID

      130000149540

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] レジームスイッチする金利のもとでの生命保険負債の経済価値評価2012

    • Author(s)
      青木, 今井
    • Organizer
      JAFEE 2011冬季大会
    • Place of Presentation
      筑波大学
    • Year and Date
      2012-03-12
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] 裾従属情報を考慮した分布境界によるポートフォリオリスクの評価2012

    • Author(s)
      宗, 今井
    • Organizer
      JAFEE 2011冬季大会
    • Place of Presentation
      筑波大学
    • Year and Date
      2012-03-12
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Optimal Cash Holdings with Dynamic Capital Structure2011

    • Author(s)
      寺本, 今井
    • Organizer
      日本リアルオプション学会(JAROS2011)
    • Place of Presentation
      青山学院大学
    • Year and Date
      2011-11-06
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Quasi-Monte Carlo method for simulating multi-dimensional Le' vy process2011

    • Author(s)
      J. Imai
    • Organizer
      The Annual Conference of Asia-Pacific Risk and Insurance Association(APRIA)
    • Place of Presentation
      Meiji University, JAPAN
    • Year and Date
      2011-08-02
    • Related Report
      2011 Final Research Report
  • [Presentation] Quasi-Monte Carlo method for simulating multi-dimensional Le'vy process2011

    • Author(s)
      Junichi Imai
    • Organizer
      The Annual Conference of Asia-Pacific Risk and Insurance Association (APRIA)
    • Place of Presentation
      Meiji University, JAPAN
    • Year and Date
      2011-08-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] Pricing exotic options with discontinuous functions using efficient quasi-Monte Carlo sampling2011

    • Author(s)
      J. Imai
    • Organizer
      15th International Congress on Insurance : Mathematics and Economics(IME2011)
    • Place of Presentation
      University of Trieste, ITALY
    • Year and Date
      2011-06-15
    • Related Report
      2011 Final Research Report
  • [Presentation] Pricing exotic options with discontinuous functions using efficient quasi-Monte Carlo sampling2011

    • Author(s)
      Junichi Imai
    • Organizer
      15th International Congress on Insurance : Mathematics and Economics (IME201l)
    • Place of Presentation
      University of Trieste, ITALY
    • Year and Date
      2011-06-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] Dimension Reduction Methods in Pricing Exotic Options under a Levy Market2011

    • Author(s)
      今井潤一
    • Organizer
      管理工学セミナー
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2011-04-20
    • Related Report
      2011 Annual Research Report
  • [Presentation] Quasi-Monte Carlo method for Levy processes via serires representations2010

    • Author(s)
      今井
    • Organizer
      JAFEE2010夏季大会
    • Place of Presentation
      成城大学
    • Year and Date
      2010-07-30
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] A numerical comparison of dimension reduction methods to simulating exotic options under a Levy market2010

    • Author(s)
      J. Imai
    • Organizer
      14th International Congress on Insurance : Mathematics and Economics
    • Place of Presentation
      University of Toronto
    • Year and Date
      2010-06-18
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Monte Carlo method for infinitely divisible random vectors and Levy process via series representations2009

    • Author(s)
      J. Imai
    • Organizer
      WatRISQ Seminar
    • Place of Presentation
      University of Waterloo, Canada
    • Year and Date
      2009-09-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Monte Carlo method for infinitely divisible random vectors and Levy process via series representations2009

    • Author(s)
      J.Imai
    • Organizer
      WatRISQ Semina
    • Place of Presentation
      University of Waterloo, Canada
    • Year and Date
      2009-09-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] A Generalized Linear Transformation Method for Simulating Meixner Levy Processes2009

    • Author(s)
      K.S.Tan
    • Organizer
      The 2009 Intemational Conference of Financial Enginee Eingineering
    • Place of Presentation
      London, U.K
    • Year and Date
      2009-07-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] A Generalized Linear Transformation Method for Simulating Meixner Levy Processes2009

    • Author(s)
      K. S. Tan and J. Imai
    • Organizer
      The 2009 International Conference of Financial Engineering
    • Place of Presentation
      London, U. K
    • Year and Date
      2009-07-02
    • Related Report
      2011 Final Research Report
  • [Presentation] The Innovator's Dilemma Under Customer Preferences Uncertainty2009

    • Author(s)
      J. Imai
    • Organizer
      The International Annual Real Options Conference 2009
    • Place of Presentation
      Minho, Portugal
    • Year and Date
      2009-06-19
    • Related Report
      2011 Final Research Report
  • [Presentation] The Innovator's Dilemma Under Customer Preferences Uncertainty2009

    • Author(s)
      J.Imai
    • Organizer
      the International Annual Real Options Conference 2009
    • Place of Presentation
      Minho, Portugal
    • Year and Date
      2009-06-19
    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.ae.keio.ac.jp/lab/soc/imai/JIMAI/index2.html

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.ae.keio.ac.jp/lab/soc/imai/JIMAI/index2.html

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.ae.keio.ac.jp/lab/soc/imai/JIMAI/index2.html

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.ae.keio.ac.jp/lab/soc/imai/JIMAI/index2.html

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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