基于拉盖尔级数展开的有限时间破产问题求解  

Solving the Finite-Time Ruin Problems by Laguerre Series Expansion

作　　者：谢佳益 张志民[1] 于文广 XIE Jiayi;ZHANG Zhimin;YU Wenguang(College of Mathematics and Statistics,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]山东财经大学保险学院,济南250014

出　　处：《应用概率统计》2022年第6期867-886,共20页Chinese Journal of Applied Probability and Statistics

基　　金：the National Natural Science Foundation of China(Grant Nos.11871121,12271066,12171405);the Shandong Provincial Natural Science Foundation(Grant Nos.ZR2022MG057,ZR2022MG027)。

摘　　要：本文研究了带扰动的复合泊松风险模型下的有限时间破产问题.我们分析了有限时间内Gerber-Shiu贴现罚函数及其分解.与拉普拉斯变换方法不同,我们利用拉盖尔级数展开提出了一个较为新颖的计算有限时间Gerber-Shiu函数的方法.当单个索赔额密度函数为有限个指数函数的混合时,我们推导了Gerber-Shiu函数的无穷级数展开式.若干数值实例验证了方法的可操作性.In this paper,we study the finite-time ruin problems in the perturbed compound Poisson risk model.The finite-time Gerber-Shiu discounted penalty function and its decomposition are studied.Different from the Laplace transform method,we propose a novel method for computing the finite-time Gerber-Shiu functions by the Laguerre series expansion.When the individual claim size density function is a finite combination of exponentials,we derive the infinite series expansions for the Gerber-Shiu functions.Some numerical examples are also given to confirm the applicability of our method.

关 键 词：有限时间Gerber-Shiu函数 拉盖尔级数展开 破产 带扰动的复合泊松风险模型 

分 类 号：O211.67[理学—概率论与数理统计]