On the renewal risk model under a threshold strategy

摘要

In this paper, we consider the renewal risk process under a threshold dividend paymentstrategy. For this model, the expected discounted dividend payments and the Gerber-Shiuexpected discounted penalty function are investigated. Integral equations, integro-differential equations and some closed form expressions for them are derived. When theclaims are exponentially distributed, it is verified that the expected penalty of the deficitat ruin is proportional to the ruin probability.