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

随机过程统计渐近理论及其在精算中的应用

• 批准号: 22500258
• 负责人: SAKAMOTO Yuji
• 金额: $ 2.75万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22500258/
• 关键词: 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

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.

研究了扩散模型基于观测值的估计问题。在观测值区间固定的情况下，得到了估计量的渐近展开式，其形式与时间序列分析的渐近展开式相似。 对于带跳的扩散过程，在遍历性或小噪声性的强条件下，证明了极大似然估计的渐近性。提出了一种检测客户风险因素指标的多重检验方法，证明了该方法在连续观测情况下保持错误发现率，并通过数值实验证明了该方法在离散观测情况下也能控制FDR。