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.

我们根据扩散模型的观察考虑了估计问题。在观察间隔固定较小的情况下，获得估计量的渐近展开式，并且它们具有与时间序列分析相似的形式。 对于具有跳跃的扩散过程，在具有遍历性或小噪声性质的强条件下证明了最大似然估计量的渐近正态性。我们提出了多重测试程序来检测客户风险因子指数，证明它在连续观察情况下保持错误发现率，并通过数值实验表明它还可以控制离散观察的FDR。