Absolute ruin problems for the risk processes with interest and a constant dividend barrier |
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Authors: | Haili Yuan Yijun Hu Qianqing Qin |
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Institution: | School of Mathematics and Statistics,Wuhan University,Wuhan 430072,Hubei,China;2.State Key Laboratory of Information Engineering in Surveying,Mapping and Remote Sensing,Wuhan University,Wuhan 430072,Hubei,China |
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Abstract: | In this paper, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated.
First, integro-differential equations satisfied by the expected discounted dividend payments are derived. The explicit expressions
are obtained when the individual claim size is exponential distributed. Second, the moment generating function of the discounted
dividends is considered, and integro-differential equations satisfied by the moment generating function of the discounted
dividends are derived. Third, by a “differential” argument, the time to recovery to zero from a given negative surplus is
considered. Finally, how long it takes for the surplus process to reach the dividend barrier is discussed. |
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Keywords: | compound Poisson risk model interest constant dividend barrier dividend payment duration |
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