Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income

被引：7

作者：

Wang, Yunyun ^{[1
]}

Yu, Wenguang ^{[2
]}

Huang, Yujuan ^{[3
]}

Yu, Xinliang ^{[2
]}

Fan, Hongli ^{[2
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

[2] Shandong Univ Finance & Econ, Sch Insurance, Jinan 250014, Shandong, Peoples R China

[3] Shandong Jiaotong Univ, Sch Sci, Jinan 250357, Shandong, Peoples R China

来源：

MATHEMATICS | 2019年 / 7卷 / 03期

基金：

中国国家自然科学基金;

关键词：

compound poisson insurance risk model; expected discounted penalty function; estimation; Fourier transform; Fourier-cosine series; FOURIER-COSINE METHOD; GERBER-SHIU FUNCTION; RUIN PROBABILITIES; DELAYED-CLAIMS; TAIL PROBABILITIES; OPTIMAL DIVIDEND; INVESTMENT; TIME; ASYMPTOTICS; STRATEGY;

D O I：

10.3390/math7030305

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider an insurance risk model with mixed premium income, in which both constant premium income and stochastic premium income are considered. We assume that the stochastic premium income process follows a compound Poisson process and the premium sizes are exponentially distributed. A new method for estimating the expected discounted penalty function by Fourier-cosine series expansion is proposed. We show that the estimation is easily computed, and it has a fast convergence rate. Some numerical examples are also provided to show the good properties of the estimation when the sample size is finite.

引用

页数：25

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