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Dividend Barrier Strategies in A Renewal Risk Model with Generalized Erlang Interarrival Times
Authors:Yuliya Mishura  Hanspeter Schmidli
Institution:1. Department of Probability Theory, Statistics and Actuarial Mathematics , National Taras Shevchenko University of Kyiv , Kyiv , Volodymyrska 64 , Ukraine;2. Department of Mathematics , University of Cologne , Weyertal 86–90 , Cologne , 50931 , Germany
Abstract: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.
Keywords:
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