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On the expected discounted penalty function in a delayed-claims risk model

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Abstract

In this paper, we consider a risk model in which each main claim may induce a delayed claim, called a by-claim. We assume that the time for the occurrence of a by-claim is random. We investigate the expected discounted penalty function, and derive the defective renewal equation satisfied by it. We obtain some explicit results when the main claim and the by-claim are both exponentially distributed, respectively. We also present some numerical illustrations.

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Authors and Affiliations

  1. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, 100081, China

    Hui Meng

  2. Department of Mathematics and Center for Financial Engineering, Soochow University, Suzhou, 215006, China

    Guo-jing Wang

Authors
  1. Hui Meng
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  2. Guo-jing Wang
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Correspondence to Hui Meng.

Additional information

The research of Hui Meng is supported by 121 Young Doctorial Development Fund Project for Central University of Finance and Economics (No. QBJJJ201004), the 2011 research grant from the China Institute for Actuarial Science, Central University of Finance and Economics and the Ministry of Education Project of Key Research Institute of Humanities and Social Sciences in Universities (No. 11JJD790004, No. 11JJD790053). The research of Guojing Wang is supported by the Natural Science Foundation (No. KB2008155) of Jiangsu Province of China and the Research Fund for the Doctorial Program of Higher Education (No. 20093201110013).

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Meng, H., Wang, Gj. On the expected discounted penalty function in a delayed-claims risk model. Acta Math. Appl. Sin. Engl. Ser. 28, 215–224 (2012). https://doi.org/10.1007/s10255-012-0141-y

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  • DOI: https://doi.org/10.1007/s10255-012-0141-y

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