Statistical Asymptotic Theory for Stochastic Processes and Its Application to Actuarial Science

• Project/Area Number: 22500258
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Kobe University
• Principal Investigator: SAKAMOTO Yuji 神戸大学, 人間発達環境学研究科, 准教授 (70215664)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 統計的漸近理論 / 確率過程 / 保険数理 / 多重検定 / 漸近展開 / 高精度確率近似 / 損害保険数理 / 状態空間モデル / 散漫初期化 / 最良線形予測 / 逐次アルゴリズム / 定常過程の推定 / 構造方程式モデル / 頑健性 / フィルタリング / 保険数理モデル

Research Abstract

We considered the estimating problem based on observations for the diffusion models. In the case where the intervals of observations are fixed small, the asymptotic expansions for estimators are obtained and they have similar form to that for time series analysis. As for the diffusion processes with jumps, the asymptotic normalities for the maximum likelihood estimators are proved under some strong conditions with ergodicity or small noise property. We proposed the multiple testing procedure to detect the customers risk factor indices, proved that it keeps false discovery rate in the continuous observation case, and show with numerical experiments that it also controls the FDR for discrete observations.