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Theory and implementation of inference for semimartingales from discrete observations.

Research Project

Project/Area Number 21740073
Research Category

Grant-in-Aid for Young Scientists (B)

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

Principal Investigator

SHIMIZU Yasutaka  大阪大学, 基礎工学研究科, 准教授 (70423085)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords統計数学 / 確率過程 / 漸近理論 / ジャンプ拡散過程 / 閾値推定 / 情報量規準 / 非エルゴード的モデル / 金融・保険への応用
Research Abstract

We developed some statistical methodologies to estimate unknown parameters in stochastic models, which is used in financial and insurance applications. The estimators are based on a set of practical data, and has a mathematical validity. The implementation to a computational package is also ongoing.

Report

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

    (43 results)

All 2012 2011 2010 2009 Other

All Journal Article (19 results) (of which Peer Reviewed: 19 results) Presentation (20 results) Remarks (4 results)

  • [Journal Article] Local asymptotic mixed normality for discretely observed non-recurrent Ornstein-Uhlenbeck processes2012

    • Author(s)
      Shimizu, Y.
    • Journal Title

      Ann. Inst. Statist. Math.

      Volume: vol.64, no.1 Pages: 193-211

    • NAID

      40019168968

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Local asymptotic mixed normality for discretely observed non-recurrent Ornstein-Uhlenbeck processes2012

    • Author(s)
      Yasutaka Shimizu
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: (印刷中) Issue: 1 Pages: 193-211

    • DOI

      10.1007/s10463-010-0307-4

    • NAID

      40019168968

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimation of parameters for discretely observed diffusion processes with a variety of rates for information2012

    • Author(s)
      Yasutaka Shimizu
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: (印刷中) Issue: 3 Pages: 545-575

    • DOI

      10.1007/s10463-010-0323-4

    • NAID

      40019169108

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimation of the expected discounted penalty function for Levy insurance risks2011

    • Author(s)
      Shimizu, Y.
    • Journal Title

      Math. Method of Statist.

      Volume: vol.20, no.2 Pages: 125-149

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 危険理論におけるGerber-Shiu関数と統計的推測2011

    • Author(s)
      清水泰隆
    • Journal Title

      統計数理

      Volume: vol.59, no.1 Pages: 105-124

    • NAID

      120006020400

    • Related Report
      2011 Annual Research Report 2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimation of the expected discounted penalty function for Levy insurance risks2011

    • Author(s)
      Yasutaka Shimizu
    • Journal Title

      Mathematical Methods of Statistics

      Volume: 20 Issue: 2 Pages: 125-149

    • DOI

      10.3103/s1066530711020037

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Local asymptotic mixed normality for discretely observed non-recurrent Ornstein-Uhlenbeck processes2011

    • Author(s)
      Yasutaka Shimizu
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: (未定)(In press)

    • NAID

      40019168968

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimation of parameters for discretely observed diffusion processes with a variety of rates for information2011

    • Author(s)
      Yasutaka Shimizu
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: (未定)(In press)

    • NAID

      40019169108

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Threshold selection in jump-discriminant filter for discretely observed jump processes2010

    • Author(s)
      Shimizu, Y.
    • Journal Title

      Statist. Methods and Appl.

      Volume: vol.19, no.3 Pages: 355-378

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Estimation of parameters for discretely observed diffusion processes with a variety of rates for information2010

    • Author(s)
      Shimizu, Y
    • Journal Title

      Ann. Inst. Statist. Math.

      Volume: vol.64, no.3 Pages: 545-575

    • NAID

      40019169108

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonparametric estimation of the Gerber-Shiu function for the Wiener-Poisson risk model2010

    • Author(s)
      Shimizu, Y.
    • Journal Title

      Scand. Actuarial Journal

      Volume: no.1 Pages: 56-69

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonparametric estimation of the Gerber-Shiu function for the Wiener-Poisson risk model2010

    • Author(s)
      Yasutaka Shimizu
    • Journal Title

      Scandinavian Actuarial Journal

      Volume: (未定)(In press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Threshold selection in jump-discriminant filter for discretely observed jump processes2010

    • Author(s)
      Yasutaka Shimizu
    • Journal Title

      Statistical Methods and Applications (In press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Notes on drift estimation for certain non-recurrent diffusion processes from sampled data2009

    • Author(s)
      Shimizu, Y.
    • Journal Title

      Statistics & Probability Letters

      Volume: vol.79, no.20 Pages: 2200-2207

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 飛躍型確率過程に対する離散観測による閾値推定法2009

    • Author(s)
      清水泰隆
    • Journal Title

      統計数理

      Volume: vol.57, no.1 Pages: 97-118

    • NAID

      120006018991

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Functional estimation for Levy measures of semimartingales with Poissonian jumps2009

    • Author(s)
      Shimizu, Y.
    • Journal Title

      J. Multivariate Anal.

      Volume: vol.100, no.6 Pages: 1073-1092

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Notes on drift estimation for certain non-recurrent diffusion processes from sampled data2009

    • Author(s)
      Yasutaka Shimizu
    • Journal Title

      Statistics & Probability Letters 79

      Pages: 2200-2207

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 飛躍型確率過程に対する離散観測による閾値推定法2009

    • Author(s)
      清水泰隆
    • Journal Title

      統計数理 57

      Pages: 97-118

    • NAID

      120006018991

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Functional estimation for Levy measures of semimartingales with Poissonian jumps2009

    • Author(s)
      Yasutaka Shimizu
    • Journal Title

      Journal of Multivariate Analysis 100

      Pages: 1073-1092

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] On estimating ruin related quantities under Levy insurance risks2011

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      STATISTICS2011 CANADA
    • Place of Presentation
      Concordia University, Canada
    • Year and Date
      2011-07-04
    • Related Report
      2011 Final Research Report
  • [Presentation] On estimating ruin related quantities under Levy insurance risks2011

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      STATISTICS2011 CANADA
    • Place of Presentation
      Concordia University (Canada)(招待講演)
    • Year and Date
      2011-07-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] Edgeworth type expansion of ruin probability under L¥'evy risk processes in the small loading asymptotics2011

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      The 15th International Congress on Insurance : Mathematics and Economics
    • Place of Presentation
      University of Trieste, Italy
    • Year and Date
      2011-06-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Edgeworth type expansion of ruin probability under Levy risk processes in the small loading asymptotics2011

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      The 15th International Congress on Insurance : Mathematics and Economics
    • Place of Presentation
      University of Trieste, Italy
    • Year and Date
      2011-06-15
    • Related Report
      2011 Final Research Report
  • [Presentation] Edgeworth type expansion of ruin probability under Levy risk processes in the small loading asymptotics2011

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      The 15th International Congress on Insurance : Mathematics and Economics
    • Place of Presentation
      University of Trieste (Italy)
    • Year and Date
      2011-06-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] Notes on estimating the probability of ruin and some generalization2011

    • Author(s)
      清水泰隆
    • Organizer
      統計数学セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2011-01-19
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Nonparametric estimation of the Gerber-Shiu function for Levy insurance risks2010

    • Author(s)
      清水泰隆
    • Organizer
      金融工学・数理・計量ファイナンスの諸問題2010
    • Place of Presentation
      大阪市中央公会堂
    • Year and Date
      2010-12-04
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Gerber-Shiu functions and the statistical inference2010

    • Author(s)
      清水泰隆
    • Organizer
      諸分野との協働による数理科学のフロンティア
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-11-19
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Gerber-Shiu functions and the statistical inference2010

    • Author(s)
      清水泰隆
    • Organizer
      統計モデルによる現象の解析,並びに,その基礎理論
    • Place of Presentation
      山形テルサ
    • Year and Date
      2010-10-23
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Nonparametric estimation of the Gerber-Shiu function for the risk process perturbed by diffusion2010

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      MATHEMATICAL FINANCE AND RELATED ISSUES
    • Place of Presentation
      京都リサーチパーク
    • Year and Date
      2010-09-13
    • Related Report
      2011 Final Research Report
  • [Presentation] Nonparametric estimation of the Gerber-Shiu function for the risk process perturbed by diffusion2010

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      WORKSHOP ON "MATHEMATICAL FINANCE AND RELATED ISSUES"
    • Place of Presentation
      京都リサーチパーク
    • Year and Date
      2010-09-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] 摂動リスクモデルに対する期待割引罰則関数の推定2010

    • Author(s)
      清水泰隆
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-09-08
    • Related Report
      2011 Final Research Report
  • [Presentation] 摂動リスクモデルに対する期待割引罰則関数の推定2010

    • Author(s)
      清水泰隆
    • Organizer
      2010年統計関連学会連合大会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-09-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] Nonparametric estimation of the Gerber-Shiu function for the risk process perturbed by diffusion2010

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      The 14th International Congress on Insurance : Mathematics and Economics
    • Place of Presentation
      University of Tronto, Canada
    • Year and Date
      2010-06-18
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Estimation of parameters for discretely observed diffusion processes with a variety of rates for information2010

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      Stochastic Analysis and Statistical Inference V
    • Place of Presentation
      東京大学
    • Year and Date
      2010-02-23
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Presentation] Quadratic type contrast functions for discretely observed non-ergodic diffusion processes2009

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      DYNSTOCH2009
    • Place of Presentation
      Humboldt-Universitat, Germany
    • Year and Date
      2009-10-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Quadratic type contrast functions for discretely observed non-ergodic diffusion processes2009

    • Author(s)
      Yasutaka Shimizu
    • Organizer
      DYNSTOCH2009
    • Place of Presentation
      Humboldt-Universitat(ドイツ)
    • Year and Date
      2009-10-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] 非エルゴード的過程の離散観測推定について2009

    • Author(s)
      清水泰隆
    • Organizer
      日本数学会,秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-26
    • Related Report
      2011 Final Research Report
  • [Presentation] 非エルゴード的過程の離散観測推定について2009

    • Author(s)
      清水泰隆
    • Organizer
      日本数学会 秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] 非再帰的OU過程に対する離散観測推定について2009

    • Author(s)
      清水泰隆
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      同志社大学
    • Year and Date
      2009-09-07
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.sigmath.es.osaka-u.ac.jp/~yasutaka/

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.sigmath.es.osaka-u.ac.jp/~yasutaka/

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.sigmath.es.osaka-u.ac.jp/~yasutaka/

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.sigmath.es.osaka-u.ac.jp/~yasutaka

    • Related Report
      2009 Annual Research Report

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

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