Dividend Barrier Strategies in A Renewal Risk Model with Generalized Erlang Interarrival Times

Abstract

We consider a renewal risk model with generalized Erlang distributed interarrival times. We assume that the phases of the interarrival time can be observed. In order to solve de Finetti's dividend problem, we first consider phasewise barrier strategies and look for the optimal barriers when the initial capital is 0. For exponentially distributed claim sizes, we show that the barrier strategy is optimal among all admissible strategies. For the special case of Erlang(2) interarrival times, we calculate the value function and the optimal barriers.