A class of Sparre Andersen risk process

Hua Dong; Zaiming Liu

doi:10.1007/s11464-010-0059-8

Front. Math. China ›› 2010, Vol. 5 ›› Issue (3) : 517 -530. DOI: 10.1007/s11464-010-0059-8

Research Article

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A class of Sparre Andersen risk process

Hua Dong ¹^,²^,^a
, Zaiming Liu ¹

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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

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Hua Dong, Zaiming Liu. A class of Sparre Andersen risk process. Front. Math. China, 2010, 5(3): 517-530 DOI:10.1007/s11464-010-0059-8

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References

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