In this paper,we consider the optimal dividend problem for a classical risk model with a constant force of interest.For such a risk model,a sufficient condition under which a barrier strategy is the optimal strategy is presented for general claim distributions.When claim sizes are exponentially distributed,it is shown that the optimal dividend policy is a barrier strategy and the maximal dividend-value function is a concave function.Finally,some known results relating to the distribution of aggregate dividends before ruin are extended.
We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend.For this risk process,we derive integral equations and exact infinite series expressions for the Gerber-Shiu discounted penalty function.Then we give lower and upper bounds for the ruin probability.Finally,we present exact expressions for the ruin probability in a special case of renewal risk processes.
