Stationary distribution of the surplus in a risk model with dividends and reinvestments

Abstract

a b s t r a c tA continuous time risk model with dividends and reinvestments is considered. We obtain an explicit formula of the stationary distribution of the surplus and the expected time to ruin after a reinvestment by adopting the level crossing argument. We also propose a scheme to approximate the stationary distribution of the surplus. As an example, we consider the case when the claims are exponentially distributed, Erlang distributed, and generalized hyperexponentially distributed.