Absolute Ruin Problems for the Risk Processes with Interest and a Constant Dividend Barrier

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.