Dividend payments until draw-down time for risk models driven by spectrally negative Lévy processes

Abstract

In this paper, a risk model driven by spectrally negative Lévy processes is considered where dividends until a general draw-down time are paid under a constant barrier strategy. In this model, the moments of the sum of the discounted dividend payments until the general draw-down time are derived through the corresponding scale functions. The explicit expressions for the Laplace transform of the discounted dividends are also obtained. Moreover, numerical examples are given to illustrate the impacts of barrier levels and draw-down functions on the results.