Development of practical inference for stochastic processes with jumps

2008 Fiscal Year Final Research Report

• Project/Area Number: 19740049
• 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 Osaka University, 基礎工学研究科, 助教 (70423085)
• Project Period (FY): 2007 – 2008
• Keywords: 確率微分方程式 / 離散観測 / パラメータ推定 / 飛躍判別フィルター / 閾値選択セミマルチンゲール / 漸近推測論

Research Abstract

飛躍構造が複合ポアソン的なジャンプ拡散過程に対する,離散観測に基づく種々の統計推測理論が構築された.飛躍判別フィルターのデータに基づく構成法がそれら理論の鍵となるが,ある特殊なモデルに対してその構成に関わる超パラメータの選択法と理論的正当性が得られた.これらの成果は,近年の金融保険数理で用いられる応用モデルの実装上,欠かせない結果であり,次のステップとなる無限ジャンプ型のモデルに対す推測論の考察の上で有益な成果と言える.

Research Products

• [Journal Article] A new aspect of a risk process and its statistical inference, Insurance (2009)
  • Author(s): 清水泰隆
  • Journal Title: Mathematics and Economics 44 Pages: 70-77
  • Peer Reviewed
• [Journal Article] Model selection for Levy measures in diffusion processes with jumps from discrete observations (2009)
  • Author(s): 清水泰隆
  • Journal Title: Journal of Statistical Planning and Inference 139 Pages: 516-532
  • Peer Reviewed
• [Journal Article] A numerical method to select the jump-detection filter for sampled jump-diffusion processes (2008)
  • Author(s): 清水泰隆
  • Journal Title: Proceedings of IASC2008 (electronic) Pages: 1417-1425
• [Journal Article] A practical inference for discretely observed jump-diffusions from finite samples (2008)
  • Author(s): 清水泰隆
  • Journal Title: Journal of Japan Statistical Society 38 Pages: 1-23
  • Peer Reviewed
• [Journal Article] Some remarks on estimation of diffusion coefficients for jump-diffusions from finite samples (2008)
  • Author(s): 清水泰隆
  • Journal Title: Bulletin of Informatics and Cybernetics 40 Pages: 51-60
  • Peer Reviewed
• [Journal Article] Statistical specification of jumps under semiparametric semimartingale models (2008)
  • Author(s): 清水泰隆
  • Journal Title: Mathematical Method of Statistics 17 Pages: 209-227
  • Peer Reviewed
• [Journal Article] Consistency of penalized risk of boosting methods in binary classification (2008)
  • Author(s): 清水泰隆, 林賢一, 狩野裕
  • Journal Title: New Trends in Psychometrics, Universal Academic Press Pages: 87-96
  • Peer Reviewed
• [Journal Article] Semiparametric estimation of Levy characteristics of jump-diffusion models from sampled data (2007)
  • Author(s): 清水泰隆
  • Journal Title: Proceedings of the Ninth Japan-China Symposium on Statistic Pages: 265-270
• [Presentation] Parametric inference for non-ergodic diffusion processes (2009)
  • Author(s): 清水泰隆
  • Organizer: Stochastic Analysis and Statistical Inference IV
  • Place of Presentation: 東京大学
  • Year and Date: 2009-02-19
• [Presentation] A numerical method to select the jump-detection filter for sampled jump-diffusion processes (2008)
  • Author(s): 清水泰隆
  • Organizer: IASC2008
  • Place of Presentation: パシフィコ横浜
  • Year and Date: 2008-12-08
• [Presentation] Threshold selection in jump-discriminant filters for infinite activity jump-diffusion models (2008)
  • Author(s): 清水泰隆
  • Organizer: Stochastic Analysis and Statistical Inference III
  • Place of Presentation: 東京大学
  • Year and Date: 2008-11-26
• [Presentation] Model selection for Levy measures in jump-diffusions by Quasi-Information Criteria (2008)
  • Author(s): 清水泰隆
  • Organizer: 日本数学会・2008年度秋季総合分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-26
• [Presentation] A practical threshold estimation for jump processes (2008)
  • Author(s): 清水泰隆
  • Organizer: Finance and related mathematical and statistical issues
  • Place of Presentation: 京都リサーチパーク
  • Year and Date: 2008-09-06
• [Presentation] Estimation of adjustment coefficients for discretely observed risk processes perturbed by diffusions (2008)
  • Author(s): Shimizu Yasutaka
  • Organizer: The 12th International Congress on Insurance : Mathematics and Economics
  • Place of Presentation: Dalian, China
  • Year and Date: 2008-07-17
• [Presentation] Ruin probability estimates for risk processes perturbed by diffusions (2008)
  • Author(s): 清水泰隆
  • Organizer: Stochastic Analysis and Statistical Inference II
  • Place of Presentation: 東京大学
  • Year and Date: 2008-02-18
• [Presentation] Detection of jumps of simple jump-diffusions from finite samples (2007)
  • 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
  • Place of Presentation: 大阪大学・中之島センター
  • Year and Date: 2007-12-02
• [Presentation] Functional estimation for Levy measures of semimartingales with Poissonian jumps (2007)
  • Author(s): 清水泰隆
  • Organizer: Stochastic Analysis and Statistical Inference
  • Place of Presentation: 東京大学
  • Year and Date: 2007-11-29
• [Presentation] Semiparametric Estimation of Levy Characteristics in Jump-Diffusion Models from Sampled Data (2007)
  • Author(s): 清水泰隆
  • Organizer: Japan-China Symposium on Statistics
  • Place of Presentation: 北海道大学
  • Year and Date: 2007-09-26
• [Presentation] 飛躍型セミマルチンゲールにおけるレヴィ測度汎関数の推定 (2007)
  • Author(s): 清水泰隆
  • Organizer: 2007年統計関連学会連合大会
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-09-08
• [Presentation] Semiparametric estimation of Levy characteristics for semimartingales with jumps from discrete observations (2007)
  • Author(s): 清水泰隆
  • Organizer: 確率的複雑系に対する漸近理論とその応用の研究
  • Place of Presentation: 大阪大学
  • Year and Date: 2007-08-09
• [Presentation] ジャンプ型確率微分方程式の有限標本によるジャンプの検出と統計的推測 (2007)
  • Author(s): 清水泰隆
  • Organizer: 応用統計ワークショップ
  • Place of Presentation: 東京大学
  • Year and Date: 2007-05-11
• [Presentation] A practical approach to the inference for jump-diffusions from finite samples (2007)
  • Author(s): Shimizu Yasutaka
  • Organizer: Statistique Asymptotique des Processus Stochastiques
  • Place of Presentation: Universite du Le Mands
  • Year and Date: 2007-03-22
• [Remarks]
  • URL: http://www.sigmath.es.osaka-u.ac.jp/~yasutaka/