CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2009, 25(5) 499-512 DOI:      ISSN: 1001-4268 CN: 31-1256

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Keywords
Sparre Andersen risk model
Erlang($n$)
Gerber-Shiu function
ruin probability.
Authors
Fan Qingzhu:Yin Chuancun
PubMed
Article by

The Gerber-Shiu Function for a Sparre Andersen\\Risk Model

Fan Qingzhu:Yin Chuancun

Department of Statistics and Finance, School of Business, Shihezi University School of Mathematical Sciences, Qufu Normal University

Abstract��

In this paper, we consider a Sparre Andersen risk model in which
the claim inter-arrival distribution is a mixture of an Erlang($n$)
distribution and an Erlang($m$) distribution. Our purpose is to
study the Gerber-Shiu function $\phi_\delta(u)$. First, we show that
$\phi_\delta(u)$ satisfies a higher-order integro-differential
equation, and then we discuss the roots of the generalized
Lundberg's equation. On this basis, we drive the Laplace transform
of $\phi_\delta(u)$ and prove that $\phi_\delta(u)$ satisfies a
renewal equation. Finally, we consider an example.

Keywords�� Sparre Andersen risk model   Erlang($n$)   Gerber-Shiu function   ruin probability.  
Received 1900-01-01 Revised 1900-01-01 Online:  
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Corresponding Authors: Fan Qingzhu
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