The bail-out optimal dividend problem under the absolutely continuous condition

摘要

This paper studies the optimal dividend problem with capital injection underthe constraint that the cumulative dividend strategy is absolutely continuous.We consider an open problem of the general spectrally negative case and derivethe optimal solution explicitly using the fluctuation identities of therefracted-reflected L\'evy process. The optimal strategy as well as the valuefunction are concisely written in terms of the scale function. Numericalresults are also given to confirm the analytical conclusions.