一种新的带扩散扰动的复合泊松模型下破产概率的非参数估计  

Nonparametric Estimation of Ruin Probability by a NewMethod in the Perturbed Compound Poisson Model

作　　者：张博 刘朝林[1,2] 于文广 李婧 ZHANG Bo;LIU Chaolin;YU Wenguang;LI Jing(College of Mathematics and Statistics,Chongqing University,Chongqing,401331,China;Provincial Experimental Teaching Demonstration Center of Mathematics of Chongqing University,Chongqing,401331,China;School of Insurance,Shandong University of Finance and Economics,Jinan,250014,China)

机构地区：[1]重庆大学数学与统计学院,重庆401331 [2]重庆大学数学省级实验教学示范中心,重庆401331 [3]山东财经大学保险学院,济南250014

出　　处：《应用概率统计》2023年第5期643-658,共16页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11871121);教育部人文社会科学研究青年基金项目“Fourier-cosine级数展开方法在风险理论中的应用”(批准号:16YJC910005);国家社会科学基金重点项目“多层次、多支柱养老保险体系构建与可持续发展研究”(批准号:21AZD071);泰山学者工程专项经费(批准号:tsqn20161041)资助。

摘　　要：本文考虑对具有扩散扰动影响的复合泊松风险模型下的破产概率进行非参数估计.我们基于复傅里叶级数展开方法 (CFS)对破产概率进行逼近,并利用索赔次数和索赔额的随机样本值对破产概率进行非参数估计.同时我们还对估计量在大样本下进行了误差分析,提供了模拟结果,验证了在样本量有限下这种估计方法的有效性.In this paper,we consider the nonparametric estimation of the ruin probability in a compound Poisson risk model perturbed by diffusion.We approximate the ruin probability based on the complex Fourier series expansion(CFS)method,and use a random sample on claim number and individual claim sizes to construct a nonparametric estimator of the ruin probability.We also perform an error analysis of the estimator under a large sample size,and provide simulation results to verify the effectiveness of this estimation method under afinite sample size.

关 键 词：破产概率 带扰动的复合泊松模型 非参数估计 CFS方法 

分 类 号：O211.9[理学—概率论与数理统计]