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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 expo-nential 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.
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. Explicit expressions are obtained when the individual claim size is is expo-nential 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.