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

Abstract

A 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. (C) 2015 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.