A class of Sparre Andersen risk process |
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Authors: | Hua Dong Zaiming Liu |
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Institution: | 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. |
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Keywords: | Sparre Andersen risk process Gerber-Shiu function Laplace transform asymptotic defective renewal equation |
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