On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes

We focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main...

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Main Authors:	Huiming Zhu, Ya Huang, Xiangqun Yang, Jieming Zhou
Format:	Article
Language:	English
Published:	Hindawi Limited 2014-01-01
Series:	Journal of Applied Mathematics
Online Access:	http://dx.doi.org/10.1155/2014/717269

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spelling	doaj-1f892215cdf544fda1bc59cabb6156ff2020-11-24T21:07:55ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/717269717269On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random IncomesHuiming Zhu0Ya Huang1Xiangqun Yang2Jieming Zhou3College of Business Administration, Hunan University, Changsha 410082, ChinaCollege of Business Administration, Hunan University, Changsha 410082, ChinaCollege of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, ChinaSchool of Mathematical Sciences, Nankai University, Tianjin 300071, ChinaWe focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process is assumed as a Poisson process. We derive the integral equation satisfied by the expected discounted penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the expected discounted penalty function is derived. Finally, for the exponential claim sizes, we present the explicit formula for the expected discounted penalty function.http://dx.doi.org/10.1155/2014/717269
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Huiming Zhu Ya Huang Xiangqun Yang Jieming Zhou
spellingShingle	Huiming Zhu Ya Huang Xiangqun Yang Jieming Zhou On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes Journal of Applied Mathematics
author_facet	Huiming Zhu Ya Huang Xiangqun Yang Jieming Zhou
author_sort	Huiming Zhu
title	On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes
title_short	On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes
title_full	On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes
title_fullStr	On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes
title_full_unstemmed	On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes
title_sort	on the expected discounted penalty function for the classical risk model with potentially delayed claims and random incomes
publisher	Hindawi Limited
series	Journal of Applied Mathematics
issn	1110-757X 1687-0042
publishDate	2014-01-01
description	We focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process is assumed as a Poisson process. We derive the integral equation satisfied by the expected discounted penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the expected discounted penalty function is derived. Finally, for the exponential claim sizes, we present the explicit formula for the expected discounted penalty function.
url	http://dx.doi.org/10.1155/2014/717269
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On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes

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