Dividend Barrier Strategies in a Renewal Risk Model With Phase-Type Distributed Interclaim Times

Linlin Tian; Zhaoyang Liu

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arXiv · 2004.08132

Dividend Barrier Strategies in a Renewal Risk Model With Phase-Type Distributed Interclaim Times

Linlin Tian·Zhaoyang Liu

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Abstract

In this paper, we consider the optimal dividend problem of the renewal risk model with phase-type distributed interclaim times and exponentially distributed claim sizes. Assume that the phases of the interclaim times can be observed. We study the optimal dividend under the 2--order and the $n$--order ($n\ge 3$)separately. In the case of 2--order phase-type distributed interclaim times, we show that the optimal dividend policy is the optimal phase-wise barrier strategy. As a byproduct, we find that in this case, the phase with higher barrier is the phase with the higher intensity to the next claim. In the case of n-order ($n\ge3$) phase-type distributed interclaim times, an iteration algorithm is presented to show that the optimal phase-wise barrier strategy is optimal among all dividend policies. We also find a similar conclusion like in the case of 2--order, the phase with the highest barrier is the phase with the highest intensity to the next claim.

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Linlin Tian, Zhaoyang Liu. 2020-04-17. Dividend Barrier Strategies in a Renewal Risk Model With Phase-Type Distributed Interclaim Times. https://arxiv.org/abs/2004.08132

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