Nonparametric estimation of risk measures of collective risks

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2015-04-10 DOI:10.1515/strm-2015-0014

A. Lauer, Henryk Zähle

引用次数: 4

Abstract

Abstract We consider two nonparametric estimators for the risk measure of the sum of n i.i.d. individual insurance risks where the number of historical single claims that are used for the statistical estimation is of order n. This framework matches the situation that nonlife insurance companies are faced with within the scope of premium calculation. Indeed, the risk measure of the aggregate risk divided by n can be seen as a suitable premium for each of the individual risks. For both estimators divided by n we derive a sort of Marcinkiewicz–Zygmund strong law as well as a weak limit theorem. The behavior of the estimators for small to moderate n is studied by means of Monte-Carlo simulations.

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集体风险风险测度的非参数估计

摘要:本文考虑了两个非参数估计量，用于估算n个个人保险风险总和的风险度量，其中用于统计估计的历史单一索赔数为n阶。该框架与非寿险公司在保费计算范围内面临的情况相匹配。实际上，总风险的风险度量除以n可以看作是每个单独风险的适当溢价。对于两个估计量除以n，我们得到了一类Marcinkiewicz-Zygmund强定律和一个弱极限定理。通过蒙特卡罗模拟研究了小到中等n估计量的行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.