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.
作者
谢佳益
张志民
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)
出处
《应用概率统计》
CSCD
北大核心
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)。
