Theory and implementation of inference for semimartingales from discrete observations.

2011 Fiscal Year Final Research Report

• Project/Area Number: 21740073
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka 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
• Keywords: 統計数学 / 確率過程 / 漸近理論

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.

Research Products

• [Journal Article] Local asymptotic mixed normality for discretely observed non-recurrent Ornstein-Uhlenbeck processes (2012)
  • Author(s): Shimizu, Y.
  • Journal Title: Ann. Inst. Statist. Math. Volume: vol.64, no.1 Pages: 193-211
  • Peer Reviewed
• [Journal Article] Estimation of the expected discounted penalty function for Levy insurance risks (2011)
  • Author(s): Shimizu, Y.
  • Journal Title: Math. Method of Statist. Volume: vol.20, no.2 Pages: 125-149
  • 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
  • Peer Reviewed
• [Journal Article] Threshold selection in jump-discriminant filter for discretely observed jump processes (2010)
  • Author(s): Shimizu, Y.
  • Journal Title: Statist. Methods and Appl. Volume: vol.19, no.3 Pages: 355-378
  • Peer Reviewed
• [Journal Article] Estimation of parameters for discretely observed diffusion processes with a variety of rates for information (2010)
  • Author(s): Shimizu, Y
  • Journal Title: Ann. Inst. Statist. Math. Volume: vol.64, no.3 Pages: 545-575
  • Peer Reviewed
• [Journal Article] Nonparametric estimation of the Gerber-Shiu function for the Wiener-Poisson risk model (2010)
  • Author(s): Shimizu, Y.
  • Journal Title: Scand. Actuarial Journal Volume: no.1 Pages: 56-69
  • Peer Reviewed
• [Journal Article] Notes on drift estimation for certain non-recurrent diffusion processes from sampled data (2009)
  • Author(s): Shimizu, Y.
  • Journal Title: Statistics & Probability Letters Volume: vol.79, no.20 Pages: 2200-2207
  • 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
  • Peer Reviewed
• [Journal Article] Functional estimation for Levy measures of semimartingales with Poissonian jumps (2009)
  • Author(s): Shimizu, Y.
  • Journal Title: J. Multivariate Anal. Volume: vol.100, no.6 Pages: 1073-1092
  • Peer Reviewed
• [Presentation] On estimating ruin related quantities under Levy insurance risks (2011)
  • Author(s): Yasutaka Shimizu
  • Organizer: STATISTICS2011 CANADA
  • Place of Presentation: Concordia University, Canada
  • Year and Date: 2011-07-04
• [Presentation] Edgeworth type expansion of ruin probability under Levy risk processes in the small loading asymptotics (2011)
  • 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
• [Presentation] Notes on estimating the probability of ruin and some generalization (2011)
  • 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
• [Presentation] Nonparametric estimation of the Gerber-Shiu function for Levy insurance risks (2010)
  • 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
• [Presentation] Gerber-Shiu functions and the statistical inference (2010)
  • 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
• [Presentation] Gerber-Shiu functions and the statistical inference (2010)
  • 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
• [Presentation] Nonparametric estimation of the Gerber-Shiu function for the risk process perturbed by diffusion (2010)
  • 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
• [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
• [Presentation] Nonparametric estimation of the Gerber-Shiu function for the risk process perturbed by diffusion (2010)
  • 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
• [Presentation] Estimation of parameters for discretely observed diffusion processes with a variety of rates for information (2010)
  • Author(s): Yasutaka Shimizu
  • Organizer: Stochastic Analysis and Statistical Inference V
  • Place of Presentation: 東京大学
  • Year and Date: 2010-02-23
• [Presentation] Quadratic type contrast functions for discretely observed non-ergodic diffusion processes (2009)
  • Author(s): Yasutaka Shimizu
  • Organizer: DYNSTOCH2009
  • Place of Presentation: Humboldt-Universitat, Germany
  • Year and Date: 2009-10-08
• [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
• [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
• [Remarks]
  • URL: http://www.sigmath.es.osaka-u.ac.jp/~yasutaka/