Absolute ruin in the compound Poisson risk model with constant dividend barrier

We investigate the absolute ruin in the compound Poisson risk model with nonnegative interest and a constant dividend barrier. An integro-differential equation satisfied by the absolute ruin probability, the distribution and moments of deficit at the time to absolute ruin is derived. In the case of exponential individual claim, the explicit expressions are given. Finally, by a “renewal” argument, which is different from the martingale approach, an integro-differential equation satisfied by the conditional probability of recovery is derived, based on which the probability of recovery is formulated. In the case of exponential individual claim, the explicit expression for the probability of recovery is also given.