Estimating the Gerber-Shiu Function in the Two-Sided Jumps Risk Model by Laguerre Series Expansion

被引：0

作者：

Hu, Kang ^{[1
]}

Huang, Ya ^{[2
]}

Deng, Yingchun ^{[3
]}

机构：

[1] Hunan Normal Univ, Sch Math & Stat, Key Lab Comp & Stochast Math, Minist Educ, Changsha 410081, Peoples R China

[2] Hunan Normal Univ, Sch Business, Changsha 410081, Peoples R China

[3] Hunan Univ Informat Technol, Sch Int Business, Changsha 410151, Peoples R China

来源：

MATHEMATICS | 2023年 / 11卷 / 09期

基金：

中国国家自然科学基金;

关键词：

two-sided jumps; Gerber-Shiu function; Laguerre series; estimator; DISCOUNTED PENALTY-FUNCTION; FOURIER-COSINE METHOD; RUIN PROBABILITY; NONPARAMETRIC-ESTIMATION; DIVIDEND PROBLEMS; VALUATION; DENSITY; TIME;

D O I：

10.3390/math11091994

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 two-sided jumps, where downward and upward jumps typically represent claim amounts and random gains, respectively. We use the Laguerre series to expand the Gerber-Shiu function and estimate it based on observed information. Moreover, we show that the estimator is easily computed and has a fast convergence rate. Numerical examples are also provided to show the efficiency of our method when the sample size is finite.

引用

页数：30

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