Ruin probabilities in the risk process with random income |
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Authors: | Zhen-hua Bao Zhong-xing Ye |
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Institution: | [1]School of Mathematics, Liaoning Normal University, Dalian 116029, China [2]Department of mathematics, Shanghai Jiaotong University, Shanghai 200240, China |
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Abstract: | We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer
a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim
times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given.
For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the
ultimate ruin probability is derived.
Supported by National Basic Research Program of China (973 Program No. 2007CB814903) and the National Natural Science Foundation
of China (No.70671069). |
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Keywords: | Beekman convolution formula Defective renewal equation Ruin probability Zero-truncated geometric distribution |
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