Frontiers of Mathematics in China >

2010 , Vol. 5 >Issue 3: 517 - 530

DOI: https://doi.org/10.1007/s11464-010-0059-8

Research articles

A class of Sparre Andersen risk process

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  • 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;

Published date: 05 Sep 2010

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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.

Key words： Sparre Andersen risk process; Gerber-Shiu function; Laplace transform; asymptotic; defective renewal equation

Cite this article

Hua DONG, Zaiming LIU, . A class of Sparre Andersen risk process[J]. Frontiers of Mathematics in China, 2010 , 5(3) : 517 -530 . DOI: 10.1007/s11464-010-0059-8

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