杨龙, 邓国和. 相依的Erlang(2)风险模型下的多段分红问题[J]. 应用概率统计, 2017, 33(1): 1-20.
引用本文: 杨龙, 邓国和. 相依的Erlang(2)风险模型下的多段分红问题[J]. 应用概率统计, 2017, 33(1): 1-20.
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YANG Long, DENG GuoHe. The Dependent Erlang(2) Risk Model with Dividend Strategy[J]. Chinese Journal of Applied Probability and Statistics, 2017, 33(1): 1-20.
Citation: YANG Long, DENG GuoHe. The Dependent Erlang(2) Risk Model with Dividend Strategy[J]. Chinese Journal of Applied Probability and Statistics, 2017, 33(1): 1-20.
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相依的Erlang(2)风险模型下的多段分红问题

The Dependent Erlang(2) Risk Model with Dividend Strategy

    摘要
  • 摘要: 本文用相依的Erlang(2) 风险模型模拟了保险公司的盈余过程, 讨论了该模型在多段分红策略下的若干问题. 首先, 期望折扣罚金函数所满足的分段的积分微分方程被给出. 然后应用该结果, 得出了其所满足的瑕疵更新方程并给出了当索赔时间间隔和索赔额的联合分布为有理分布时该方程的解. 本文的结论深化了精算学中一些已有研究成果.

     

    Abstract: In this paper, an Erlang(2) risk model with time-dependent claims is studied under a multi-layer dividend strategy. First, some piecewise integro-differential equations with certain boundary conditions for the Gerber-Shiu function are derived. Then, applying these results, some defective renewal equations and explicit expressions for the Gerber-Shiu function are obtained when the joint density of the inter-claim time and claim size belongs to the rational family.

     

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