A class of Sparre Andersen risk process

doi:10.1007/s11464-010-0059-8

Front. Math. China

2010, Vol. 5

Issue (3) : 517-530 https://doi.org/10.1007/s11464-010-0059-8

Research articles

A class of Sparre Andersen risk process

Hua DONG¹,Zaiming LIU²,

1.School of Mathematics, Central South University, Changsha 410075, China；School of Mathematics, Qufu Normal University, Qufu 273165, China; 2.School of Mathematics, Central South University, Changsha 410075, China;

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Abstract In this paper, we investigate a renewal risk model in which the distribution of the interclaim times is a mixture of two Erlang distributions. First, the Laplace transform and the defective renewal equation for the Gerber-Shiu function are derived. Then, two asymptotic results for the Laplace transform of the time of ruin are given when the initial surplus tends to infinity for the light-tailed claims and heavy-tailed claims, respectively. Finally, an explicit expression for the Gerber-Shiu function is given.

Keywords Sparre Andersen risk process Gerber-Shiu function Laplace transform asymptotic defective renewal equation

Issue Date: 05 September 2010

Cite this article:

Hua DONG,Zaiming LIU. A class of Sparre Andersen risk process[J]. Front. Math. China, 2010, 5(3): 517-530.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-010-0059-8
https://academic.hep.com.cn/fmc/EN/Y2010/V5/I3/517

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