On the Gerber–Shiu discounted penalty function in a risk model with two types of delayed-claims and random income
作者：
Highlights：
• We develop a new delayed model with random premium income and two types of by-claims.
• We derive an integral equations system for Gerber–Shiu discounted penalty function.
• We get an explicit solution to Laplace transform of the discounted penalty function.
• We prove the discounted penalty function satisfying a defective renewal equation.
• We get an explicit result of the ruin probability under the exponential distribution.
摘要
•We develop a new delayed model with random premium income and two types of by-claims.•We derive an integral equations system for Gerber–Shiu discounted penalty function.•We get an explicit solution to Laplace transform of the discounted penalty function.•We prove the discounted penalty function satisfying a defective renewal equation.•We get an explicit result of the ruin probability under the exponential distribution.
论文关键词：By-claim,Auxiliary model,Laplace transform,Rouché theorem,Lagrange interpolation theorem
论文评审过程：Received 6 November 2013, Available online 25 March 2014.
论文官网地址：https://doi.org/10.1016/j.cam.2014.03.011
