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2007 Fiscal Year Final Research Report Summary

Analysis of Wiener functional and derivative pricing

Research Project

Project/Area Number 17540107
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHitotsubashi University

Principal Investigator

FUJITA Takahiko  Hitotsubashi University, Graduate School of Commerce and Management, Professor (50144316)

Project Period (FY) 2005 – 2007
Keywordsrandom walk / Brownian motion / Bessel process / Exotic option / Black Scholes model / Infinitely divisible distribution / Cauchy distrbution / Riemann zeta function
Research Abstract

(1)On research of exotic options written by rank statistics
(2)On distribution theory for fragments of random walk , Brownian motion and Bessel processe straddling independent Exponential times
(3)A stochastic approach to special values of the Riemann zeta function
(4)On research of orderstatistics
(5)On research of new exotic derivative products (meander option)
Especially, with Bertoin, J., Yor, M. and Roynette, B., I obtained the explicit calculation of the distribution of fragments of random walk, Brownian motion, Bessel processe straddling independent exponential times and the infinitely divisibility of such distributions, of which Levy Hintchin measure is a kind of arcsine laws.
straddling independent exponential times and the infinitely divisibility of such distributions, of which Levy Hintchin mesure is a kind of aresine laws.

  • Research Products

    (36 results)

All 2008 2007 2006 2005 Other

All Journal Article (16 results) (of which Peer Reviewed: 7 results) Presentation (19 results) Book (1 results)

  • [Journal Article] A proof of Ito's formula using a discrete Ito's formula2008

    • Author(s)
      Takahiko Fujita and Yasuhiro Kawanishi
    • Journal Title

      Studia Scientiarum Mathematicarum Hungarica 45-1

      Pages: 125-134

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Euler's formulae for the Riemann zeta function and Cauchy variables2008

    • Author(s)
      Takahiko Fujita
    • Journal Title

      The Institute of Statistical Mathematics Cooperative Research Report 213

      Pages: 98-103

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] A proof of Ito's formula using a discrete Ito's formula Studia Scientiarum2008

    • Author(s)
      Takahiko, Fuiita, Yasuhiro, Kawanishi
    • Journal Title

      Mathematicarum Hungaria 45-1

      Pages: 125-134

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Euler's formulae for the Rieman seta function and Cauchy variables2008

    • Author(s)
      Takahiko, Fujita
    • Journal Title

      The Institute of Statistical Mathematics Cooperative 213

      Pages: 98-103

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Euler formulae for zeta(2n)and Cauchy variables2007

    • Author(s)
      Bourgade, , P., Fujita, T., Yor, M.
    • Journal Title

      Electronic Communications in Probability Theory 12

      Pages: 73-80

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] On the infinite divisibility and the selfdecomposability of length of random walk, Brownian and Bessel excursions straddling independent exponential times2007

    • Author(s)
      Fujita, T., Yor, M.
    • Journal Title

      統計数理研究所共同研報告集無限分解可能分布に関する諸問題(11) 195

      Pages: 126-134

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On the remarkable distributions of maxima of some fragments of the standard reflecting random walk and Brownian Motion2007

    • Author(s)
      Takahiko FUJITA and Marc Yor
    • Journal Title

      Probability and Mathematical Statistics 27-1

      Pages: 89-104

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] A warning about an independent property related to Random Brownian scaling2007

    • Author(s)
      Takahiko FUJITA and Marc Yor
    • Journal Title

      Probability and Mathematical Statistics 27-1

      Pages: 105-108

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] On the infinite divisibility and the selfdecomposability of length of random walk2007

    • Author(s)
      Fujita, T., Yor, M
    • Journal Title

      Toukei Suuri Kennkyuusho Kyudoukenn houkokushoshuu Mugennbunnkai kanoubunnpu ni kannsuru shomonndai(11) 195

      Pages: 126-134

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On the remarkable distributions of maxima of some fragments of the standard reflecting random walk and Brownian Motion2007

    • Author(s)
      Takahiko, FUJITA, Marc, Yor
    • Journal Title

      Probability and Mathematical Statistics 27-1

      Pages: 89-104

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A warning about an independent property related to Random Brownian scaling2007

    • Author(s)
      Takahiko, FUJITA, Marc, Yor
    • Journal Title

      Probability and Mathematical Statistics 27-1

      Pages: 105-108

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The distribution of continuous time rank processes2006

    • Author(s)
      Takahiko FUJITA and Ryozo Miura
    • Journal Title

      Advances in Mathematical Economics 9

      Pages: 1-8

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] On a particular class of self-decomposable random variables: the durations of Bessel excursions straddling independent exponential times2006

    • Author(s)
      Bertoin. J., Fujita, T., Roynette, B., Yor, M
    • Journal Title

      Probability and Methematical Statistics Vol.26,issue2

      Pages: 315-366

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] The distribution of continuous time rank processes2006

    • Author(s)
      Takahiko, FUJITA, Ryozo, MIURA
    • Journal Title

      Advances in Mathematical Economics 9

      Pages: 1-8

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On a particular class of self-Statistics26-2 Decomposable random variables: the durations of Bessel excurations Straddling independent exponential times2006

    • Author(s)
      Bertoin, J., Fuiita, T., Roynette, B., Yor, M
    • Journal Title

      Probability and Mathematical

      Pages: 315-366

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Euler formulae for zeta(2n) and Cauchy variables

    • Author(s)
      Bourgade, P., Fujita, T., Roynette, B., Yor, M
    • Journal Title

      Electronic Communications in Probab

    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] On new exotic derivative products2007

    • Author(s)
      Fujita, T.
    • Organizer
      新金融商品開発展望検討会
    • Place of Presentation
      台湾、台北、政治大学
    • Year and Date
      2007-12-08
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] On new exotic derivatice products2007

    • Author(s)
      Fujita, T
    • Organizer
      Shin knnyuushouhin kaihatsu tennbou kenntoukai
    • Place of Presentation
      Taiwann Taipei Seijidaigaku
    • Year and Date
      2007-12-08
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] On the pricing of neander option2007

    • Author(s)
      Fujita, T.
    • Organizer
      金融工学数理ファイナンスとその応用シンポジウム
    • Place of Presentation
      大阪 大阪大学
    • Year and Date
      2007-12-01
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] On the pricing of neander option2007

    • Author(s)
      Fujita, T
    • Organizer
      Klnnyuukougaku suuri Fainannce to sono ouyou shinnpojium
    • Place of Presentation
      Osaka, Osakadaigaku
    • Year and Date
      2007-12-01
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Special values of the Riemann zeta function and Cauchy variables2007

    • Author(s)
      Fujita, T
    • Organizer
      Mugenn bunnkai kanoubunnpuronn to sono ouyou
    • Place of Presentation
      Tokyo, Toukeisuuri kennkyuusho
    • Year and Date
      2007-11-15
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Special values of the Riemann zeta function and Cauchy variables2007

    • Author(s)
      Fujita, T.
    • Organizer
      無限分解可能分布論とその応用
    • Place of Presentation
      東京、統計数理研究所
    • Year and Date
      2007-11-05
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] A Probabilistic approach to special values of the Riemann zeta2007

    • Author(s)
      Fujita, T.
    • Organizer
      数論と確率論国際シンポジウム
    • Place of Presentation
      奈良、高等研究所
    • Year and Date
      2007-10-16
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] A Probabilistic approach to special values of the Riemann zeta2007

    • Author(s)
      Fujita, T
    • Organizer
      Suuron to kakuritsu ronn kokusai shinnpojiumm
    • Place of Presentation
      Nara, Koutoukennkyuusho
    • Year and Date
      2007-10-16
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] 離散確率解析とその周辺、-リーマン・ゼータからブラック・ショールズまで-2007

    • Author(s)
      Fujita, T.
    • Organizer
      日本数学会 企画特別講演
    • Place of Presentation
      日本、埼玉大学
    • Year and Date
      2007-03-27
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Risan Kakuritsu Kaisekito sono Shuuhen Rimann.Zeta kara Black shouruzu made2007

    • Author(s)
      Fujita, T
    • Organizer
      Nihonnsuugakukai kikaku tokubetsu kouenn
    • Place of Presentation
      Nihon Saitam daigaku
    • Year and Date
      2007-03-27
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] A probabistic approach to special values of the Riemann zeta function2007

    • Author(s)
      Fujita, T.
    • Organizer
      エルゴード理論と数論シンポジウム
    • Place of Presentation
      金沢 金沢大学
    • Year and Date
      2007-02-10
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] A probabistic Approach to special values of the Riemann zeta function2007

    • Author(s)
      Fujita, T
    • Organizer
      Erugodo riron to suuron shinnpojium
    • Place of Presentation
      Kanazawa Kanazawadaigaku
    • Year and Date
      2007-02-10
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] On the price of meander options and related topics2007

    • Author(s)
      Fujita, T.
    • Organizer
      数理ファイナンスとその周辺シンポジウム
    • Place of Presentation
      駒場、東京大学数理科学研究科
    • Year and Date
      2007-01-25
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] On the price of Meander options and related topics2007

    • Author(s)
      Fujita, T
    • Organizer
      Suuri fainannce to sono shuuhenn shinnpojium
    • Place of Presentation
      Komaba, Tokyoudaigaku suuri kagaku kennkyuuka
    • Year and Date
      2007-01-25
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] On the infinitely divisibility and the self-decomposability of the lengh of excursions of Random walk, Brownian, Bessel processes straddling independent exponential times2006

    • Author(s)
      Fujita, T.
    • Organizer
      無限分解可能分布論とその応用
    • Place of Presentation
      東京、統計数理研究所
    • Year and Date
      2006-11-15
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] On the infinitely divisibility and the self-decomposability of the lengh of excursions of Randon walk, Brownian, Bessel processes straddling independent exponential times2006

    • Author(s)
      Fujita, T
    • Organizer
      Mugenbunkai kanou bunnpu to sono ouyou
    • Place of Presentation
      Tokyo, Toukei suuri Kennkyuusho
    • Year and Date
      2006-11-15
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] On the infinitely divisibility and the self-decomposability of the lengh of excursions of Random walk, Brownian, Bessel processes straddling independent exponential times2006

    • Author(s)
      Fujita, T.
    • Organizer
      Oidemase Yamaguchi Probability Sinpojium
    • Place of Presentation
      Japan, Yamaguchi
    • Year and Date
      2006-11-12
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] On the remarkable distributions of Brownian and Random walk fragments2005

    • Author(s)
      Fujita, T.
    • Organizer
      Journee des Probabilites
    • Place of Presentation
      France, Univ. of Nancy
    • Year and Date
      2005-09-02
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] On the remarkable distributions of Brownian and Random walk fragments France, Univ. of Nancy2005

    • Author(s)
      Fujita, T
    • Organizer
      Journee des Probabilites
    • Year and Date
      2005-09-02
    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] 道具としての金融工学2005

    • Author(s)
      藤田岳彦
    • Total Pages
      256
    • Publisher
      日本実業出版社
    • Description
      「研究成果報告書概要(和文)」より

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Published: 2010-02-04  

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