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2014 On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes
Huiming Zhu, Ya Huang, Xiangqun Yang, Jieming Zhou
J. Appl. Math. 2014: 1-12 (2014). DOI: 10.1155/2014/717269

Abstract

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.

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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." J. Appl. Math. 2014 1 - 12, 2014. https://doi.org/10.1155/2014/717269

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010722
MathSciNet: MR3178967
Digital Object Identifier: 10.1155/2014/717269

Rights: Copyright © 2014 Hindawi

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