具有阶段型分布索赔时间的更新风险模型的红利壁垒策略
Dividend Barrier Strategies in a Renewal Risk Model With Phase-Type Distributed Interclaim Times
摘要：
本文考虑索赔额为指数分布且索赔间隔时间为阶段型分布的更新风险模型的最优分红问题。假设可以观察到索赔间隔时间的阶段。本文分别研究了2阶和$n$阶（$n\ge 3$）下的最优分红问题.在2阶相型分布的索赔时间的情况下，我们证明了最优股息政策是最优的阶段障碍策略。作为副产品，我们发现，在这种情况下，具有较高势垒的相位是下一个声明具有较高强度的相位。在n阶（$n\ge3$）相位型分布索赔间隔时间的情形下，给出了一个迭代算法，证明了最优相位屏障策略在所有分红策略中是最优的.我们也发现了类似的结论，就像在2阶的情况下，具有最高势垒的相位是到下一个声明具有最高强度的相位。
英文摘要：
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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