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.
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页数：30
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